A176631 Triangle T(n, k) = 22^(k*(n-k)), read by rows.

1, 1, 1, 1, 22, 1, 1, 484, 484, 1, 1, 10648, 234256, 10648, 1, 1, 234256, 113379904, 113379904, 234256, 1, 1, 5153632, 54875873536, 1207269217792, 54875873536, 5153632, 1, 1, 113379904, 26559922791424, 12855002631049216, 12855002631049216, 26559922791424, 113379904, 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, k) = Product_{j=1..n} (q*(3*q - 1)/2)^j and q = 4.

T(n, k, q) = (binomial(3*q, 2)/3)^(k*(n-k)) with q = 4.

T(n, k, m) = (m+2)^(k*(n-k)) with m = 20. - G. C. Greubel, Jul 01 2021

Example

Triangle begins as:
  1;
  1,       1;
  1,      22,           1;
  1,     484,         484,             1;
  1,   10648,      234256,         10648,           1;
  1,  234256,   113379904,     113379904,      234256,       1;
  1, 5153632, 54875873536, 1207269217792, 54875873536, 5153632, 1;

Mathematica

T[n_, k_, q_]= (Binomial[3*q, 2]/3)^(k*(n-k)); Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten
Table[22^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Jul 01 2021 *)

Prog

(Magma) [22^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 01 2021
(Sage) flatten([[22^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jul 01 2021

Crossrefs

Cf. A000326.

Cf. A118190 (q=2), A176627 (q=3), this sequence (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), A176643 (m=19), this sequence (m=20), A176641 (m=26), A176644 (m=38).

Sequence in context: A291074 A225076 A022185 * A015150 A040493 A040494

Adjacent sequences: A176628 A176629 A176630 * A176632 A176633 A176634

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 22 2010

Extensions

Edited by G. C. Greubel, Jul 01 2021

Status

approved