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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 those of [1, 2].
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Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, Arxiv arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.
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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
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
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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.
Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, Arxiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.
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allocated for N. J. A. Sloane
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 those 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
0,2
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.
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nonn
N. J. A. Sloane, Apr 07 2012
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