A125102 Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,k+1)/2 (0<=k<=n).

1, 2, 2, 3, 6, 3, 4, 12, 10, 4, 5, 20, 22, 18, 5, 6, 30, 40, 50, 26, 6, 7, 42, 65, 110, 81, 38, 7, 8, 56, 98, 210, 196, 140, 50, 8, 9, 72, 140, 364, 406, 392, 204, 66, 9, 10, 90, 192, 588, 756, 924, 624, 306, 82, 10, 11, 110, 255, 900, 1302, 1932, 1590, 1050, 415, 102, 11, 12

Offset

0,2

Comments

Binomial transform of the bidiagonal matrix with (1,2,3...) in the main diagonal and (1,2,1,2,1,2...) in the subdiagonal. Sum of terms in row n = (n+5)*2^(n-1)-2 for n>=1.

Links

Table of n, a(n) for n=0..66.

Example

First few rows of the triangle are:
1;
2, 2;
3, 6, 3;
4, 12, 10, 4;
5, 20, 22, 18, 5;
6, 30, 40, 50, 26, 6;
7, 42, 65, 110, 81, 38, 7;
...

Maple

T:=(n, k)->(k+1)*binomial(n, k)+(3-(-1)^k)*binomial(n, k+1)/2: for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form

Crossrefs

Sequence in context: A291543 A296320 A296396 * A003506 A047662 A329655

Adjacent sequences: A125099 A125100 A125101 * A125103 A125104 A125105

Keyword

nonn,tabl

Author

Gary W. Adamson, Nov 20 2006

Extensions

Edited by N. J. A. Sloane, Nov 29 2006

Status

approved