The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A210425 Number of 3-divided words of length n over a 4-letter alphabet. 2
 0, 0, 4, 60, 374, 1960, 9103, 40497, 174127, 735268, 3064477, 12664101, 52005445, 212595280, 866047122 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS See A210109 for further information. Row sums of the following table which shows how many words of length n over a 4-letter alphabet are 3-divided in k>=1 different ways: 4; 41, 14, 5; 147, 111, 67, 29, 14, 6; 594, 358, 381, 211, 156, 128, 80, 28, 17, 7; 2072, 1400, 1433, 875, 821, 669, 588, 369, 340, 240, 163, 72, 33, 20, 8; - R. J. Mathar, Mar 25 2012 LINKS Table of n, a(n) for n=1..15. PROG (Python) from itertools import product def is3div(b): for i in range(1, len(b)-1): for j in range(i+1, len(b)): X, Y, Z = b[:i], b[i:j], b[j:] if all(b < bp for bp in [X+Z+Y, Z+Y+X, Y+X+Z, Y+Z+X, Z+X+Y]): return True return False def a(n): return sum(is3div("".join(b)) for b in product("0123", repeat=n)) print([a(n) for n in range(1, 9)]) # Michael S. Branicky, Aug 30 2021 CROSSREFS Cf. A210109, A210426. Sequence in context: A060492 A234952 A112041 * A366690 A002060 A247739 Adjacent sequences: A210422 A210423 A210424 * A210426 A210427 A210428 KEYWORD nonn AUTHOR R. J. Mathar, Mar 21 2012 EXTENSIONS a(12)-a(15) from Michael S. Branicky, Aug 30 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 25 16:30 EDT 2024. Contains 372801 sequences. (Running on oeis4.)