A164045 a(n+1) = 5*a(n) - n.

1, 4, 18, 87, 431, 2150, 10744, 53713, 268557, 1342776, 6713870, 33569339, 167846683, 839233402, 4196166996, 20980834965, 104904174809, 524520874028, 2622604370122, 13113021850591, 65565109252935, 327825546264654

Offset: 0

Author

Rolf Pleisch, Aug 08 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7, -11, 5).

Programs

Mathematica

Table[(11*5^n + 4*n + 5)/16, {n,0,50}] (* G. C. Greubel, Sep 08 2017 *)
LinearRecurrence[{7,-11,5},{1,4,18},30] (* or *) nxt[{n_,a_}]:={n+1,5a-n-1}; NestList[nxt,{0,1},30][[;;,2]] (* Harvey P. Dale, Sep 29 2023 *)

PARI

a(n) = (11*5^n + 4*n + 5)/16 \\ Michel Marcus, Jul 18 2013

Formula

a(0)=1; a(n+1) = 5*a(n) - n.

a(n) = (11*5^n + 4*n + 5)/16.

From R. J. Mathar, Aug 09 2009: (Start)

a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).

G.f.: (1-3*x+x^2)/((1-5*x)*(1-x)^2). (End)

E.g.f.: (1/16)*(11*exp(5*x) + (4*x + 5)*exp(x)). - G. C. Greubel, Sep 08 2017