A104882 Diagonal sums of number triangle A104881.

1, 1, 2, 3, 5, 8, 14, 24, 45, 85, 170, 351, 749, 1656, 3758, 8776, 21013, 51473, 129018, 329939, 860901, 2288528, 6192526, 17047248, 47693661, 135554549, 391099370, 1144867871, 3398656893, 10226072720, 31173964942, 96240485104, 300777706053

Offset: 0

Author

Paul Barry, Mar 28 2005

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A104879, A104881.

Programs

Magma

[(&+[ (&+[ (n-2*k)^(k-j) : j in [0..k]]) : k in [0..Floor(n/2)]]): n in [0..40]]; // G. C. Greubel, Jun 15 2021

Mathematica

Table[Sum[If[j==k, 1, (n-2*k)^(k-j)], {k, 0, Floor[n/2]}, {j,0,k}], {n,0,40}] (* G. C. Greubel, Jun 15 2021 *)

Sage

[sum(sum((n-2*k)^(k-j) for j in (0..k)) for k in (0..n//2)) for n in (0..40)] # G. C. Greubel, Jun 15 2021

Formula

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

a(n) = Sum_{k=0..floor(n/2)} A104881(n-k, k).