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 A176642 Triangle T(n, k) = 8^(k*(n-k)), read by rows. 14
 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, 1, 2097152, 68719476736, 35184372088832, 281474976710656, 35184372088832, 68719476736, 2097152, 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, 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 Cf. this sequence (q=2), A176643 (q=3), A176644 (q=4). Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), this sequence (m=6), A158117 (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26). Cf. A000567, A004247. Sequence in context: A340560 A022171 A203443 * A172346 A178048 A174728 Adjacent sequences: A176639 A176640 A176641 * A176643 A176644 A176645 KEYWORD nonn,tabl,less,easy AUTHOR Roger L. Bagula, Apr 22 2010 EXTENSIONS Edited by R. J. Mathar and G. C. Greubel, Jun 30 2021 STATUS approved

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Last modified March 2 10:43 EST 2024. Contains 370466 sequences. (Running on oeis4.)