A053308 Partial sums of A053296.

1, 9, 46, 175, 551, 1518, 3785, 8735, 18955, 39130, 77533, 148487, 276408, 502415, 895103, 1568062, 2708322, 4622488, 7811510, 13091798, 21791338, 36067176, 59419294, 97522270, 159571139, 260459265, 424302452, 690141333

Offset: 0

Author

Barry E. Williams, Mar 06 2000

Keywords

• easy
• nonn

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-35,76,-98,70,-14,-20,19,-7,1).

Crossrefs

Cf. A053296, A053295, A136431.

Cf. A228074.

Programs

Magma

[(&+[Binomial(n+8-j, n-2*j): j in [0..Floor(n/2)]]): n in [0..30]]; // G. C. Greubel, May 24 2018

Mathematica

Table[Sum[Binomial[n+8-j, n-2j], {j, 0, Floor[n/2]}], {n, 0, 50}] (* G. C. Greubel, May 24 2018 *)

PARI

for(n=0, 30, print1(sum(j=0, floor(n/2), binomial(n+8-j, n-2*j)), ", ")) \\ G. C. Greubel, May 24 2018

Formula

a(n) = Sum_{i=0..floor(n/2)} C(n+8-i, n-2i), n >= 0.

a(n) = a(n-1) + a(n-2) + C(n+7,7); n >= 0; a(-1)=0.