Sequential circuit with more than 10 LEDs
If they can all be on the same amount of time, I'd just use lots of shift registers. There are several types. For your application look for Serial In, Parallel Out (SIPO).

If it mattered how bright the LEDs are, and you want very bright, use 'proper' LED display drivers.

For example TI Display drivers

They come in 8-LED, 16-LED and even 24-LED devices.

A SIPO shift register can be chained together by driving them all from a common clock, and connecting Serial Out of one device to Serial In of the next device. They may also have an enable which trasfers the shifted bit pattern into the LED drivers.

Initialisation, power on, must clear all of them to zero (usually a RESET), and initially load a 1 to the first shift register.

Edit: Removed concerns about 4017, as they don't apply.

A datasheet for 4017 which shows  a schematic for cascading three (and hence more) 4017 in Figure 12 page 15.