A202690 - OEIS

%I #20 Jun 03 2020 03:45:39

%S 1,1,0,1,1,2,4,4,3,3,2,0,0,4,8,11,11,14,16,16,80,80,76,68,57,57,46,32,

%T 16,0,0,80,160,236,304,361,361,418,464,496,512,512,3904,3904,3824,

%U 3664,3428,3124,2763,2763,2402,1984,1520,1024,512,0

%N The triangle in A185356 with the central column of zeros omitted.

%H M. Josuat-Vergès, J.-C. Novelli and J.-Y. Thibon, <a href="http://arxiv.org/abs/1110.5272">The algebraic combinatorics of snakes</a>, arXiv preprint arXiv:1110.5272 [math.CO], 2011.

%e Triangle begins:

%e                      1 1

%e                  0   1 1   2

%e              4   4   3 3   2   0

%e          0   4   8  11 11  14  16  16

%e     80  80  76  68  57 57  46  32  16  0

%e   0 80 160 236 304 361 361 418 464 496 512 512

%o (PARI) T(n,k) = {if ((k==0), return(0)); if (n==1, if (abs(k)==1, return(1))); if (n%2, if (k<0, sum(j=k+1, n-1, T(n-1,j)), sum(j=k, n-1, T(n-1,j))), if (k<0, sum(j=-n+1, k, T(n-1,j)), sum(j=-n+1, k-1, T(n-1,j))));}

%o tabf(nn) = {for (n=1, nn, for (k=-n, n, if (k, print1(T(n, k), ", "));); print;);} \\ _Michel Marcus_, Jun 03 2020

%Y Cf. A185356, A202691, A202704.

%K nonn,tabf

%O 1,6

%A _N. J. A. Sloane_, Dec 22 2011

%E More terms from _Michel Marcus_, Jun 03 2020