A234357 Array A(n,k) by ascending antidiagonals: A(n,k) = n^k * Fibonacci(k + 1) for n, k >= 1.

1, 2, 2, 3, 8, 3, 4, 18, 24, 5, 5, 32, 81, 80, 8, 6, 50, 192, 405, 256, 13, 7, 72, 375, 1280, 1944, 832, 21, 8, 98, 648, 3125, 8192, 9477, 2688, 34, 9, 128, 1029, 6480, 25000, 53248, 45927, 8704, 55, 10, 162, 1536, 12005, 62208, 203125, 344064, 223074, 28160, 89

Offset

1,2

Links

Table of n, a(n) for n=1..55.

Formula

G.f. of n-th row: 1/(1 - n*x - n^2*x^2).

Recurrence: A(n,k) = n*A(n,k-1) + n^2*A(n,k-2), starting n, 2*n^2.

Example

Array starts:
  1,  2,   3,    5,     8,     13,    21,   34, 55, 89,...    (A000045)
  2,  8,  24,   80,   256,    832,  2688, 8704,...   (A063727, A085449)
  3, 18,  81,  405,  1944,   9477, 45927,...         (A122069, A099012)
  4, 32, 192, 1280,  8192,  53248,...                         (A099133)
  5, 50, 375, 3125, 25000, 203125,...
  6, 72, 648, 6480, 62208, 606528,...
  ...

Prog

(PARI) A(n, k)=n^k*fibonacci(k + 1)
(PARI) A(n, k)=polcoeff(Ser(1/(1-n*x-n^2*x^2)), k)

Crossrefs

Columns k=1..3 give A000027, A001105, A117642.

Sequence in context: A296804 A296952 A141611 * A145596 A186753 A135835

Adjacent sequences: A234354 A234355 A234356 * A234358 A234359 A234360

Keyword

nonn,tabl

Author

Ralf Stephan, Dec 24 2013

Extensions

Offset and definition corrected by Georg Fischer, Nov 17 2025

Status

approved