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A061897
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.
2
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, 162, 96, 40, 12, 2, 0, 0, 128, 486, 328, 150, 54, 14, 2, 0, 0, 256, 1458, 1120, 550, 220, 70, 16, 2, 0, 0, 512, 4374, 3824, 2000, 858, 308, 88, 18, 2, 0, 0, 1024, 13122, 13056
OFFSET
0,3
FORMULA
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.
EXAMPLE
Rows start
1, 0, 0, 0, 0, ...
2, 0, 0, 0, 0, ...
2, 4, 8, 16, 32, ...
2, 6, 18, 54, 162, ...
2, 8, 28, 96, 328, ...
...
CROSSREFS
Cf. A060995. Rows include A000007, A000038, A000079, A008776, A060995. Columns effectively (i.e. except for a small number of terms) include A040000, A005843, A028552.
Sequence in context: A024164 A138805 A316400 * A372568 A047919 A272624
KEYWORD
nonn,tabl
AUTHOR
Henry Bottomley, May 14 2001
STATUS
approved