A106264 Diagonal sums of number triangle A106262.

1, 0, 1, 2, 2, 4, 2, 4, 6, 7, 7, 8, 14, 10, 13, 12, 15, 19, 22, 22, 23, 25, 25, 44, 44, 40, 28, 50, 44, 54, 52, 55, 50, 66, 53, 72, 83, 80, 58, 73, 82, 110, 114, 123, 127, 113, 91, 112, 158, 137, 117, 122, 152, 135, 166, 160, 211, 206, 171, 219, 240, 201, 188, 194, 236

Offset: 0

Author

Paul Barry, Apr 28 2005

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A106262.

Programs

Magma

[(&+[2^(n-2*k) mod (k+2): k in [0..Floor(n/2)]]): n in [0..80]]; // G. C. Greubel, Jan 10 2023

Mathematica

Table[Sum[Mod[2^(n-2*k), k+2], {k,0,Floor[n/2]}], {n,0,80}] (* G. C. Greubel, Jan 10 2023 *)

SageMath

def A106264(n): return sum( (2^(n-2*k)%(k+2)) for k in range(n//2+1) )
[A106264(n) for n in range(81)] # G. C. Greubel, Jan 10 2023

Formula

a(n) = Sum_{k=0..floor(n/2)} ( 2^(n-2*k) mod (k+2) ).