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A053308 Partial sums of A053296. 5
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

Table of n, a(n) for n=0..27.

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

lst={}; s0=s1=s2=s3=s4=s5=s6=s7=0; Do[s0+=a[n]; s1+=s0; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; AppendTo[lst, s7], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 10 2008 *)

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,changed

AUTHOR

Barry E. Williams, Mar 06 2000

STATUS

approved

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Last modified February 21 21:41 EST 2018. Contains 299427 sequences. (Running on oeis4.)