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

Author

Gary W. Adamson, Aug 09 2007

Keywords

• nonn
• easy
• tabl

Examples

			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;
...
		

Links

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

Crossrefs

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

Programs

Magma

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

Mathematica

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

Formula

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