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A158117
Triangle T(n, k) = 10^(k*(n-k)), read by rows.
14
1, 1, 1, 1, 10, 1, 1, 100, 100, 1, 1, 1000, 10000, 1000, 1, 1, 10000, 1000000, 1000000, 10000, 1, 1, 100000, 100000000, 1000000000, 100000000, 100000, 1, 1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1
OFFSET
0,5
FORMULA
T(n, k, q) = c(n,q)/(c(k,q)*c(n-k,q)) where c(n, k) = binomial(q+2, 2)^binomial(n+1, 2), c(n, 0) = n!, and q = 3.
T(n, k, q) = binomial(q+2, 2)^(k*(n-k)) with q = 3.
T(n, k, m) = (m+2)^(k*(n-k)) with m = 8. - G. C. Greubel, Jun 30 2021
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 10, 1;
1, 100, 100, 1;
1, 1000, 10000, 1000, 1;
1, 10000, 1000000, 1000000, 10000, 1;
1, 100000, 100000000, 1000000000, 100000000, 100000, 1;
1, 1000000, 10000000000, 1000000000000, 1000000000000, 10000000000, 1000000, 1;
MATHEMATICA
(* First program *)
T[n_, k_, q_]= Binomial[q+2, 2](k*(n-k));
Table[T[n, k, 3], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jun 30 2021 *)
(* Second program *)
With[{m=8}, Table[(m+2)^(k*(n-k)), {n, 0, 12}, {k, 0, n}]//Flatten] (* G. C. Greubel, Jun 30 2021 *)
PROG
(Magma) [10^(k*(n-k)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jun 30 2021
(Sage) flatten([[10^(k*(n-k)) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jun 30 2021
CROSSREFS
Cf. A007318 (q=0), A118180 (q=1), A158116 (q=2), this sequence (q=3), A176639 (q=4), A176643 (q=5), A176641 (q=6).
Cf. A117401 (m=0), A118180 (m=1), A118185 (m=2), A118190 (m=3), A158116 (m=4), A176642 (m=6), this sequence (m=8), A176627 (m=10), A176639 (m=13), A156581 (m=15), A176643 (m=19), A176631 (m=20), A176641 (m=26).
Sequence in context: A160562 A176243 A022173 * A172378 A015124 A156767
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Mar 12 2009
EXTENSIONS
Edited by G. C. Greubel, Jun 30 2021
STATUS
approved