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A176631 Triangle T(n, k) = 22^(k*(n-k)), read by rows. 9
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 5 01:17 EDT 2022. Contains 357240 sequences. (Running on oeis4.)