A127159 Triangle T(n,k) with T(n,k) = A061554(n,k) + A107430(n,k).

2, 2, 2, 3, 2, 3, 4, 4, 4, 4, 7, 5, 8, 5, 7, 11, 11, 10, 10, 11, 11, 21, 16, 21, 12, 21, 16, 21, 36, 36, 28, 28, 28, 28, 36, 36, 71, 57, 64, 36, 56, 36, 64, 57, 71, 127, 127, 93, 93, 72, 72, 93, 93, 127, 127, 253, 211, 220, 130, 165, 90, 165, 130, 220, 211, 253

Offset: 0

Author

Philippe Deléham, Mar 25 2007

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   2;
   2,  2;
   3,  2,  3;
   4,  4,  4,  4;
   7,  5,  8,  5,  7;
  11, 11, 10, 10, 11, 11;
  21, 16, 21, 12, 21, 16, 21;
  36, 36, 28, 28, 28, 28, 36, 36;
  71, 57, 64, 36, 56, 36, 64, 57, 71; ...
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A061554, A107430.

Programs

GAP

Flat(List([0..12], n-> List([0..n], k-> Binomial(n, Int((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Int(k/2)) ))); # G. C. Greubel, Jan 31 2020

Magma

[Binomial(n, Floor((n+1 -(-1)^(n-k)*(k+1))/2)) + Binomial(n, Floor(k/2)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 31 2020

Maple

seq(seq( binomial(n, floor((n+1-(-1)^(n-k)*(k+1))/2)) +binomial(n, floor(k/2)), k=0..n), n=0..12); # G. C. Greubel, Jan 31 2020

Mathematica

T[n_, k_]= Binomial[n, Floor[(n+1 -(-1)^(n-k)*(k+1))/2]] + Binomial[n, Floor[k/2]]; Table[T[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Jan 31 2020 *)

PARI

T(n,k) = binomial(n, (n+1 -(-1)^(n-k)*(k+1))\2 ) + binomial(n, k\2); \\ G. C. Greubel, Jan 31 2020

Sage

[[binomial(n, floor((n+1 -(-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jan 31 2020

Formula

Sum_{k=0..n} T(n,k) = 2^(n+1).

T(n, k) = binomial(n, floor((n+1 - (-1)^(n-k)*(k+1))/2)) + binomial(n, floor(k/2)). - G. C. Greubel, Jan 31 2020