A132108 Triangle T(n,k) = binomial(n,k)+n-k read by rows.

1, 2, 1, 3, 3, 1, 4, 5, 4, 1, 5, 7, 8, 5, 1, 6, 9, 13, 12, 6, 1, 7, 11, 19, 23, 17, 7, 1, 8, 13, 26, 39, 38, 23, 8, 1, 9, 15, 34, 61, 74, 59, 30, 9, 1, 10, 17, 43, 90, 131, 130, 87, 38, 10, 1

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..5000

Formula

T(n,k) = A007318(n,k) + A002024(n,k) - A002260(n,k).

Example

First few rows of the triangle are:
1;
2, 1;
3, 3, 1;
4, 5, 4, 1;
5, 7, 8, 5, 1;
6, 9, 13, 12, 6, 1;
7, 11, 19, 23, 17, 7, 1;
...

Mathematica

Table[Binomial[n, k]+n-k, {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Mar 08 2018 *)

Prog

(Magma) /* As triangle: */ [[Binomial(n, k)+n-k: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, May 23 2016

Crossrefs

Cf. A007318, A002024, A002260, A132109 (row sums).

Sequence in context: A208721 A208777 A104732 * A377000 A210489 A344821

Adjacent sequences: A132105 A132106 A132107 * A132109 A132110 A132111

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Aug 09 2007

Status

approved