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

Author

Richard Choulet, Jan 31 2010

Keywords

• easy
• nonn

Links

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

Crossrefs

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

Partial sums of A104144.

Programs

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 *)

Formula

G.f.: 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).