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A053309 Partial sums of A053308. 4
1, 10, 56, 231, 782, 2300, 6085, 14820, 33775, 72905, 150438, 298925, 575333, 1077748, 1972851, 3540913, 6249235, 10871723, 18683233, 31775031, 53566369, 89633545, 149052839, 246575109, 406146248, 666605513, 1090907965 (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..26.

Index entries for linear recurrences with constant coefficients, signature (10,-44,111,-174,168,-84,-6,39,-26,8,-1).

FORMULA

a(n) = Sum_{i=0..floor(n/2)} C(n+9-i, n-2i), n >= 0.

a(n) = Sum_{k=1..n} C(n-k+9,k+8), with n>=0. - Paolo P. Lava, Apr 16 2008

G.f.: 1/((x^2 + x - 1)*(x-1)^9). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009

EXAMPLE

a(n) = a(n-1) + a(n-2) + C(n+8,8); n >= 0; a(-1)=0.

MATHEMATICA

lst={}; s0=s1=s2=s3=s4=s5=s6=s7=s8=0; Do[s0+=a[n]; s1+=s0; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; s7+=s6; s8+=s7; AppendTo[lst, s8], {n, 0, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Dec 10 2008 *)

CROSSREFS

Cf. A053296, A053295, A136431.

Cf. A228074.

Sequence in context: A296918 A001786 A258478 * A035040 A002889 A055911

Adjacent sequences:  A053306 A053307 A053308 * A053310 A053311 A053312

KEYWORD

easy,nonn,changed

AUTHOR

Barry E. Williams, Mar 06 2000

STATUS

approved

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Last modified February 23 23:15 EST 2018. Contains 299595 sequences. (Running on oeis4.)