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

Author

Richard Choulet, Jan 31 2010

Keywords

• easy
• nonn

Examples

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

Links

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

Crossrefs

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

Partial sums of A079262.

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

Formula

G.f.: 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).