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A164045
a(n+1) = 5*a(n) - n.
2
1, 4, 18, 87, 431, 2150, 10744, 53713, 268557, 1342776, 6713870, 33569339, 167846683, 839233402, 4196166996, 20980834965, 104904174809, 524520874028, 2622604370122, 13113021850591, 65565109252935, 327825546264654
OFFSET
0,2
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
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 *)
PROG
(PARI) a(n) = (11*5^n + 4*n + 5)/16 \\ Michel Marcus, Jul 18 2013
CROSSREFS
Sequence in context: A111966 A225887 A153294 * A178577 A130524 A298646
KEYWORD
nonn
AUTHOR
Rolf Pleisch, Aug 08 2009
STATUS
approved