A211276 a(n) = number of n-lettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 1] as of [1, 2].

1, 3, 7, 18, 47, 123, 328, 886, 2419, 6675, 18587, 52164, 147404, 418991, 1197002, 3434568, 9891715, 28580469, 82808899, 240511642, 700024987, 2041255981, 5962023006, 17439034426, 51075928264, 149767494573, 439619556301, 1291671623988, 3798447661874, 11179106282223, 32925086562548

Offset

0,2

Links

Table of n, a(n) for n=0..30.

Shalosh B. Ekhad and Doron Zeilberger, Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.

Formula

Conjecture: n*a(n) +2*(-3*n+1)*a(n-1) +(7*n+6)*a(n-2) +2*(7*n-37)*a(n-3) +3*(-7*n+40)*a(n-4) +6*(-n-4)*a(n-5) +27*(-n+6)*a(n-6) +54*(n-6)*a(n-7)=0. - R. J. Mathar, May 31 2014

Crossrefs

Sequence in context: A027969 A027971 A219233 * A018028 A045994 A101308

Adjacent sequences: A211273 A211274 A211275 * A211277 A211278 A211279

Keyword

nonn

Author

N. J. A. Sloane, Apr 07 2012

Status

approved