A147840 a(n)=10*a(n-1)-8*a(n-2), a(0)=1, a(1)=8 .

1, 8, 72, 656, 5984, 54592, 498048, 4543744, 41453056, 378180608, 3450181632, 31476371456, 287162261504, 2619811643392, 23900818341888, 218049690271744, 1989290355982336, 18148506037649408, 165570737528635392

Offset: 0

Author

Philippe Deléham, Nov 14 2008

Keywords

• nonn
• easy

Comments

a(n) = sum_{k=0..n} 2^n*binomial(n,k)*A007482(k) = 2^n*A052913(n). - R. J. Mathar, Oct 15 2012

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-8).

Programs

Mathematica

LinearRecurrence[{10,-8},{1,8},20] (* Harvey P. Dale, Dec 02 2021 *)

Formula

a(n)=Sum_{k, 0<=k<=n}A147703(n,k)*7^k . G.f.: (1-2x)/(1-10x+8*x^2).

a(n)= ((17+3*sqrt(17))/34)*(5+sqrt(17))^n + ((17-3*sqrt(17))/34)*(5-sqrt(17))^n [From Richard Choulet, Nov 20 2008]

G.f.: (1-2x)/(1-10x+8x^2). - Harvey P. Dale, Dec 02 2021