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.

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

Links

Table of n, a(n) for n=0..70.

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

Adjacent sequences: A061894 A061895 A061896 * A061898 A061899 A061900

Keyword

nonn,tabl

Author

Henry Bottomley, May 14 2001

Status

approved