Search: id:A071922
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%I A071922
%S A071922 1,1,1,1,2,1,1,3,4,1,1,4,9,7,1,1,5,16,22,11,1,1,6,25,50,46,16,1,1,7,36,
%T A071922 95,130,86,22,1,1,8,49,161,295,296,148,29,1,1,9,64,252,581,791,610,239,
%U A071922 37,1,1,10,81,372,1036,1792,1897,1163,367,46,1,1,11,100,525,1716,3612
%N A071922 Unimodal analogue of binomial coefficient, such that A071921(n,m)=a(n+m-1,
               n) for all (n,m) different from (0,0), arranged in a Pascal-like 
               triangle.
%C A071922 Also, number of n-length k-ary words avoiding the pattern 1'-2-1". - 
               Ralf Stephan, Apr 28 2004
%H A071922 S. Kitaev and T. Mansour, <a href="http://arXiv.org/abs/math.CO/0210023">
               Partially ordered generalized patterns and k-ary words</a>.
%F A071922 a(n, m)=sum_{k=0}^{n-m} binomial(2k+m-1, 2k).
%F A071922 sum_{m=0}^n a(n, m)=1+F_{2n}, where F_n is the n-th Fibonacci number.
%F A071922 sum_{m=0}^n (-1)^m a(n, m)=1 if 3 divides n, 0 otherwise.
%F A071922 G.f. for k-th row: 1/(1-x)^(2k-1) + sum[j=1..k-1, x/(1-x)^(2j)]. - Ralf 
               Stephan, Apr 28 2004
%t A071922 a[n_, m_] := Sum[ Binomial[2k + m - 1, 2k], {k, 0, n - m}]; Flatten[ 
               Table[ a[n, m], {n, 0, 11}, {m, 0, n}]]
%Y A071922 Sequence in context: A122084 A104559 A080853 this_sequence A138028 A009999 
               A144823
%Y A071922 Adjacent sequences: A071919 A071920 A071921 this_sequence A071923 A071924 
               A071925
%K A071922 nonn,easy,tabl
%O A071922 0,5
%A A071922 Michele Dondi (bik.mido(AT)tiscalinet.it), Jun 14, 2002
%E A071922 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 17 2002

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