A173031 Sequence whose G.f is given by: 1/(1-z)/(1-2*z)^2/(1-z-z^2).

1, 6, 24, 79, 232, 632, 1633, 4058, 9788, 23063, 53332, 121452, 273089, 607534, 1339376, 2929951, 6366480, 13752880, 29556545, 63232370, 134731956, 286044711, 605326044, 1277246724, 2687879137, 5642847462, 11820387528, 24710992303

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Index entries for linear recurrences with constant coefficients, signature (6,-12,7,4,-4).

Formula

a(n+5) = 6*a(n+4)-12*a(n+3)+7*a(n+2)+4*a(n+1)-4*a(n).

a(n) = (38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n.

a(n) = F(n+8)+2^(n+3)*(n-4)-1, where (F(n)) is the Fibonacci sequence for which F(0)=F(1)=1, F(2)=2, ... (related to A000045).

Maple

c(0):=1:c(1):=6:c(2):=24:c(3):=79:c(4):=232:for n from 0 to 30 do : c(n+5):=6*c(n+4)-12*c(n+3)+7*c(n+2)+4*c(n+1)-4*c(n): od :seq(c(n), n=0..30); taylor((-1/(-1+z)/(-1+2*z)^2/(1-z-z^2)), z=0, 30); for n from 0 to 30 do a(n):=simplify((38/5*5^(1/2)+17)*((1+sqrt(5))/2)^n+(-38/5*5^(1/2)+17)*((1-sqrt(5))/2)^n-32*2^n-1+16*2^(n-1)*n):od:seq(a(n), n=0..30);

Crossrefs

Sequence in context: A140088 A359133 A011855 * A350413 A361474 A004404

Adjacent sequences: A173028 A173029 A173030 * A173032 A173033 A173034

Keyword

easy,nonn

Author

Richard Choulet, Feb 07 2010

Status

approved