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A164044
a(n+1) = 4*a(n) - n.
3
1, 3, 10, 37, 144, 571, 2278, 9105, 36412, 145639, 582546, 2330173, 9320680, 37282707, 149130814, 596523241, 2386092948, 9544371775, 38177487082, 152709948309, 610839793216, 2443359172843, 9773436691350, 39093746765377
OFFSET
0,2
FORMULA
a(0)=1; a(n+1) = 4*a(n) - n.
a(n) = (5*4^n + 3*n + 4)/9.
From R. J. Mathar, Aug 09 2009: (Start)
a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3).
G.f.: (1-3*x+x^2)/((1-4*x)*(1-x)^2). (End)
E.g.f.: (1/9)*(5*exp(4*x) + (3*x + 4)*exp(x)). - G. C. Greubel, Sep 08 2017
MATHEMATICA
Table[(5*4^n + 3*n + 4)/9, {n, 0, 50}] (* G. C. Greubel, Sep 08 2017 *)
PROG
(PARI) x='x+O('x^50); Vec((1-3*x+x^2)/((1-4*x)*(1-x)^2)) \\ G. C. Greubel, Sep 08 2017
CROSSREFS
Sequence in context: A219260 A151050 A151051 * A119244 A151052 A264231
KEYWORD
nonn
AUTHOR
Rolf Pleisch, Aug 08 2009
STATUS
approved