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A176643
Triangle T(n, k) = 21^(k*(n-k)), read by rows.
9
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
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
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Apr 22 2010
EXTENSIONS
Edited by G. C. Greubel, Jul 01 2021
STATUS
approved