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A053308 Partial sums of A053296. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

FORMULA

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

a(n) = Sum_{k=1..n} C(n-k+8,k+7), with n>=0. - Paolo P. Lava, Apr 16 2008

EXAMPLE

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

MATHEMATICA

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

PROG

(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

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

CROSSREFS

Cf. A053296, A053295, A136431.

Cf. A228074.

Sequence in context: A260513 A001781 A258477 * A201458 A034487 A035039

Adjacent sequences:  A053305 A053306 A053307 * A053309 A053310 A053311

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Mar 06 2000

STATUS

approved

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Last modified October 17 19:36 EDT 2018. Contains 316293 sequences. (Running on oeis4.)