A172319 10th column of A172119.

1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1023, 2044, 4084, 8160, 16304, 32576, 65088, 130048, 259840, 519168, 1037313, 2072582, 4141080, 8274000, 16531696, 33030816, 65996544, 131863040, 263466240, 526413312, 1051789311

Offset

0,2

Links

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

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

Formula

G.f f such that: f(z)=1/(1-2*z+z^10).

a(n)=sum((-1)^j*binomial(n-k*j,n-(k+1)*j)*2^(n-(k+1)*j),j=0..floor(n/(k+1))). a(n+10)=2*a(n+9)-a(n).

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;

Mathematica

LinearRecurrence[{2, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 2, 4, 8, 16, 32, 64, 128, 256, 512}, 40] (* Harvey P. Dale, Sep 22 2020 *)

Crossrefs

Cf. A172318, A172317, A172316, A172119, A001949, A107066.

Sequence in context: A051535 A008862 A145116 * A234591 A122265 A339073

Adjacent sequences: A172316 A172317 A172318 * A172320 A172321 A172322

Keyword

easy,nonn

Author

Richard Choulet, Jan 31 2010

Status

approved