Code words in integer sequences Introduction

Pareidolia: From Ancient Greek; παρα ‎(para, “concurrent, alongside”) + εἴδωλον ‎(eídōlon, “image”). The tendency to interpret a vague stimulus as something known to the observer, such as interpreting marks on Mars as canals, seeing shapes in clouds, or hearing hidden messages in music. Source: Wiktionary.

For example:



Paralogia: From Ancient Greek; παρα ‎(para, “concurrent, alongside”) + λόγος ‎(lógos, “speech, oration, word, ...”). The tendency to perceive words in arbitrary sequences of characters, such as in code golf programs. Source: yeah, I made that up (actually the word means something else, as pointed out by @Martin).

For example:

    df4$/H)hEy_^p2\
    jtK2$)look|x1$


Challenge

Write a program that takes a positive integer as input, produces an integer as output, and includes an English word as part of the code. The input-output relationship must correspond to an integer sequence that can be found in OEIS.

Rules


Only words from this list are allowed. This is admittedly arbitrary, but it's essential that we all agree on which words are accepted; and in that regard this list is probably as good as any other.
Words need to be formed by concatenating at least two function names or statements. If your language for example has a function called correlation it can't be used as is. The concatenation has to be strict: no other symbols should appear between the parts of the word. For example, bro~ken would not count as a word.
Case is unimportant: both valid and vaLiDare acceptable.
Words within strings do not count. The letters that make up the word need to be functions or statements in the language of choice, that is, something that is actually executed. For example, the following code would not be allowed: 'deoxyribonucleic'~1, where '...' is a string, ~ discards the previous content, and 1 just prints number 1.
Every letter of the word should be necessary. This means that removing a single letter from the word should change the input-output relation. That includes outputting a different sequence, or outputting any other thing(s), or producing no output, or causing an error.
Any positive integer should be acceptable as an input, and should produce an output, except for data-type or memory restrictions.
The outputs corresponding to inputs 1, 2, 3, ... should correspond to a sequence appearing in OEIS. No other output should be produced; only an integer number, possibly with trailing or leading whitespace.
Input and output can be function arguments or stdin/stdout.


Score

The score is computed as total code length minus twice the length of the longest word, in characters. Or equivalently, number of not-in-longest-word characters minus length of longest word.

Lowest score wins.

Examples

Consider an imaginary postfix language that has these functions: c: input a number; At: compute square; $: add 1.

cAt would be a valid program (its output corresponds to the sequence 1, 4, 9, ..., which is A000290), and it would have score −3.

cAt$ would also be valid (sequence 2, 5, 10, ..., which is A002522), with score −2.

c$At would not be valid, because the only word here is "At" and is produced by a single function or statement.
CJam, -20
COUNTErREVOLUTIONARIES],

Outputs the nth element in the sequence A010861.
COUNTE                      e# push values of six preinitialized variables
      r                     e# read a token of input
       REVOLUTIONARIES      e# push values of 15 other preinitialized variables
                      ]     e# wrap whole stack in array
                       ,    e# get length

Removing a character from the word results in a completely different sequence A010860. There is a quite interesting relationship between the two sequences: at every index n, A010860(n) is coprime to A010861(n)! There must be some deep mathematical reason behind this.
Try it here.