A176643 Triangle T(n, k) = 21^(k*(n-k)), read by rows.

1, 1, 1, 1, 21, 1, 1, 441, 441, 1, 1, 9261, 194481, 9261, 1, 1, 194481, 85766121, 85766121, 194481, 1, 1, 4084101, 37822859361, 794280046581, 37822859361, 4084101, 1, 1, 85766121, 16679880978201, 7355827511386641, 7355827511386641, 16679880978201, 85766121, 1

Offset

0,5

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k, q) = c(n,q)/(c(k, q)*c(n-k, q)) where c(n, q) = (q*(3*q - 2))^binomial(n+1,2) and q = 3.

T(n, k, q) = (q*(3*q-2))^(k*(n-k)) with q = 3.

T(n, k, m) = (m+2)^(k*(n-k)) with m = 19. - G. C. Greubel, Jul 01 2021

Example

Triangle begins as:
  1;
  1,       1;
  1,      21,           1;
  1,     441,         441,            1;
  1,    9261,      194481,         9261,           1;
  1,  194481,    85766121,     85766121,      194481,       1;
  1, 4084101, 37822859361, 794280046581, 37822859361, 4084101, 1;

Mathematica

T[n_, k_, q_]:= (q*(3*q-2))^(k*(n-k)); Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten
Table[21^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 01 2021 *)

Prog

(Magma) [(21)^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 01 2021
(Sage) flatten([[(21)^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 01 2021

Crossrefs

Cf. A000567.

Cf. A176642 (q=2), this sequence (q=3), A176644 (q=4).

Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), A176642 (m=6), A158117 (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), this sequence (m=19), A176631 (m=20), A176641 (m=26).

Sequence in context: A291073 A172301 A022184 * A015147 A174945 A040450

Adjacent sequences: A176640 A176641 A176642 * A176644 A176645 A176646

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 22 2010

Extensions

Edited by G. C. Greubel, Jul 01 2021

Status

approved