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 = 2.
T(n, k, q) = (q*(3*q-2))^(k*(n-k)) with q = 2.
T(n, k) = 8^A004247(n,k), where A004247 is interpreted as a triangle. [relation detected by sequencedb.net]. - R. J. Mathar, Jun 30 2021
T(n, k, m) = (m+2)^(k*(n-k)) with m = 6. - G. C. Greubel, Jun 30 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 8, 1;
1, 64, 64, 1;
1, 512, 4096, 512, 1;
1, 4096, 262144, 262144, 4096, 1;
1, 32768, 16777216, 134217728, 16777216, 32768, 1;
1, 262144, 1073741824, 68719476736, 68719476736, 1073741824, 262144, 1;
MATHEMATICA
T[n_, k_, q_]:= (q*(3*q-2))^(k*(n-k)); Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten
With[{m=6}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(Magma) [8^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[8^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 22 2010
EXTENSIONS
Edited by R. J. Mathar and G. C. Greubel, Jun 30 2021
STATUS
approved