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
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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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
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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).