OFFSET
0,2
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).
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
KEYWORD
nonn
AUTHOR
Rolf Pleisch, Aug 08 2009
STATUS
approved