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A172317 8th column of A172119. 4
1, 2, 4, 8, 16, 32, 64, 128, 255, 508, 1012, 2016, 4016, 8000, 15936, 31744, 63233, 125958, 250904, 499792, 995568, 1983136, 3950336, 7868928, 15674623, 31223288, 62195672, 123891552, 246787536, 491591936, 979233536 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..30.

Index entries for linear recurrences with constant coefficients, signature (2,0,0,0,0,0,0,-1).

FORMULA

The generating function is f such that: f(z)=1/(1-2*z+z^8). Recurrence relation: a(n+8)=2*a(n+7)-a(n). General term: a(n) = Sum_{j=0..floor(n/(k+1))} ((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j)) with k=7.

EXAMPLE

a(4) = binomial(4,4)*2^4 = 16.

a(9) = binomial(9,9)*2^9 - binomial(2,1)*2^1 = 512 - 4 = 508.

MAPLE

k:=7:taylor(1/(1-2*z+z^(k+1)), z=0, 30); for k from 0 to 20 do for n from 0 to 30 do b(n):=sum((-1)^j*binomial(n-k*j, n-(k+1)*j)*2^(n-(k+1)*j), j=0..floor(n/(k+1))):od:k: seq(b(n), n=0..30):od;

CROSSREFS

Cf. A172316, A001949, A107066, A008937, A172119.

Sequence in context: A054045 A008860 A145114 * A234589 A079262 A194631

Adjacent sequences:  A172314 A172315 A172316 * A172318 A172319 A172320

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Jan 31 2010

STATUS

approved

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)