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

0,3

Links

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

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).

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 *)

Prog

(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
(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

Crossrefs

Cf. A104879, A104881.

Sequence in context: A108296 A072100 A290075 * A091956 A107480 A345235

Adjacent sequences: A104879 A104880 A104881 * A104883 A104884 A104885

Keyword

easy,nonn

Author

Paul Barry, Mar 28 2005

Status

approved