A141596 Triangle T(n,k) = 4*binomial(n,k)^2-3, read by rows, 0<=k<=n.

1, 1, 1, 1, 13, 1, 1, 33, 33, 1, 1, 61, 141, 61, 1, 1, 97, 397, 397, 97, 1, 1, 141, 897, 1597, 897, 141, 1, 1, 193, 1761, 4897, 4897, 1761, 193, 1, 1, 253, 3133, 12541, 19597, 12541, 3133, 253, 1, 1, 321, 5181, 28221, 63501, 63501, 28221, 5181, 321, 1, 1, 397, 8097

Offset

0,5

Comments

Row sums are: 1, 2, 15, 68, 265, 990, 3675, 13704, 51453, 194450, 738991, ... = 4*binomial(2n,n) -3*(n+1).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..10000

Example

1;
1, 1;
1, 13, 1;
1, 33, 33, 1;
1, 61, 141, 61, 1;
1, 97, 397, 397, 97, 1;
1, 141, 897, 1597, 897, 141, 1;
1, 193, 1761, 4897, 4897, 1761, 193, 1;
1, 253, 3133, 12541, 19597, 12541, 3133, 253, 1;
1, 321, 5181, 28221, 63501, 63501, 28221, 5181, 321, 1;
1, 397, 8097, 57597, 176397, 254013, 176397, 57597, 8097, 397, 1;

Mathematica

Clear[t, n, m, k, l] t[n_, m_, k_, l_] := (1 + l)*Binomial[n, m]^k - l; k = 2; l = 3; Table[Table[t[n, m, k, l], {m, 0, n}], {n, 0, 10}]; Flatten[%]
Table[4Binomial[n, k]^2-3, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Dec 21 2016 *)

Crossrefs

Cf. A109128.

Sequence in context: A066834 A010225 A060361 * A108477 A176204 A176492

Adjacent sequences: A141593 A141594 A141595 * A141597 A141598 A141599

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Aug 21 2008

Status

approved