A172318 9th column of the array A172119.

1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1020, 2036, 4064, 8112, 16192, 32320, 64512, 128768, 257025, 513030, 1024024, 2043984, 4079856, 8143520, 16254720, 32444928, 64761088, 129265151, 258017272, 515010520, 1027977056

Offset

0,2

Links

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

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

Formula

G.f.: f such that: f(z)=1/(1-2*z+z^9).

a(n) = sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))) with k=8.

Recurrence relation: a(n+9) = 2*a(8) - a(n).

Example

a(7)=C(7,7)*2^7=128. a(10)=C(10,10)*2^10-C(2,1)*2^1=1020.

Maple

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; k:=8:taylor(1/(1-2*z+z^(k+1)), z=0, 30);

Crossrefs

Cf. A172317, A172316, A172119, A001949, A107066.

Sequence in context: A054046 A008861 A145115 * A234590 A104144 A258800

Adjacent sequences: A172315 A172316 A172317 * A172319 A172320 A172321

Keyword

easy,nonn

Author

Richard Choulet, Jan 31 2010

Status

approved