A298800 Triangle read by rows: T(n,k) = number of Ringel ladders of order n and genus k.

2, 14, 2, 38, 24, 2, 70, 184, 2, 118, 648, 256, 2, 198, 1656, 2240, 2, 342, 3752, 9728, 2560, 2, 614, 8152, 31168, 25600, 2, 1142, 17544, 86784, 132096, 24576, 2, 2182, 37816, 225728, 504320, 278528, 2, 4246, 81768, 566784, 1649152, 1662976, 229376, 2, 8358, 177048, 1393600, 4945920, 7335936, 2916352

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Esther Hunt Tesar, Genus distribution of Ringel ladders, Discrete Mathematics 216.1-3 (2000): 235-252.

Example

Triangle begins:
  2, 14,
  2, 38, 24,
  2, 70, 184,
  2, 118, 648, 256,
  2, 198, 1656, 2240,
  2, 342, 3752, 9728, 2560,
  2, 614, 8152, 31168, 25600,
  ...

Prog

(PARI) T(n, k) = 2^(3*k+1)*binomial(n-k, k) + 2^(3*k)*binomial(n-k, k-1) + (2^(n+k) - 2^(3*k-3))*binomial(n-k+1, k-2) + (2^(n+k+1) - 2^(3*k-2))*binomial(n-k+1, k-1);
tabf(nn) = {for(n=1, nn, for(k=0, ceil((n+1)/2), print1(T(n, k), ", "); ); print(); ); }; \\ Michel Marcus, May 24 2018

Crossrefs

Sequence in context: A221234 A133420 A227628 * A138907 A336837 A276189

Adjacent sequences: A298797 A298798 A298799 * A298801 A298802 A298803

Keyword

nonn,tabf

Author

N. J. A. Sloane, Feb 02 2018

Extensions

Corrected and extended by Michel Marcus, May 24 2018

Status

approved