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%I #9 Nov 18 2022 03:39:16
%S 1,0,2,0,0,2,0,0,4,2,0,0,8,6,2,0,0,16,18,8,2,0,0,32,54,28,10,2,0,0,64,
%T 162,96,40,12,2,0,0,128,486,328,150,54,14,2,0,0,256,1458,1120,550,220,
%U 70,16,2,0,0,512,4374,3824,2000,858,308,88,18,2,0,0,1024,13122,13056
%N Square table by antidiagonals of number of routes of length 2k+n on the sides of a 2n-gon from a point to its opposite point.
%F T(0, 0)=1; if n>0, T(n, 0)=2; if k>1, T(n, k)=T(n, k-1)*A061896(n, 1)-T(n, k-2)*A061896(n, 2)+T(n, k-3)*A061896(n, 3)-T(n, k-4)*A061896(n, 4)+...T(n, k-[n/2])*A061896(n, [n/2]); if 0>k T(n, k)=0.
%e Rows start
%e 1, 0, 0, 0, 0, ...
%e 2, 0, 0, 0, 0, ...
%e 2, 4, 8, 16, 32, ...
%e 2, 6, 18, 54, 162, ...
%e 2, 8, 28, 96, 328, ...
%e ...
%Y Cf. A060995. Rows include A000007, A000038, A000079, A008776, A060995. Columns effectively (i.e. except for a small number of terms) include A040000, A005843, A028552.
%K nonn,tabl
%O 0,3
%A _Henry Bottomley_, May 14 2001
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