OFFSET
1,2
REFERENCES
Mario Velucchi "From the desk of ... Mario Velucchi" in 'Mathematics and Informatics quarterly' volume 7 - 2/1997, p. 81.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..650
Index entries for linear recurrences with constant coefficients, signature (41,-246,246,-41,1).
FORMULA
From R. J. Mathar, Apr 15 2010: (Start)
G.f.: x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)).
a(n) = 41*a(n-1) -246*a(n-2) +246*a(n-3) -41*a(n-4) +a(n-5). (End)
Lim_{n -> infinity} a(n)/a(n-1) = A156164. - César Aguilera, Jul 17 2020
EXAMPLE
a(3) = 525 = 15*35 = 15 + 16 + ... + 35.
MAPLE
MATHEMATICA
LinearRecurrence[{41, -246, 246, -41, 1}, {1, 18, 525, 17340, 586177}, 20] (* Paul Cleary, Dec 05 2015 *)
CoefficientList[Series[(-1 + 23*x - 33*x^2 + 3*x^3)/((x - 1)*(x^2 - 34*x + 1)*(1 - 6*x + x^2)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 16 2017 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)) )); // G. C. Greubel, Oct 18 2024
(SageMath)
def A011906_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(1-23*x+33*x^2-3*x^3)/((1-x)*(1-34*x+x^2)*(1-6*x+x^2)) ).list()
a=A011906_list(30); a[1:] # G. C. Greubel, Oct 18 2024
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Mario Velucchi (mathchess(AT)velucchi.it)
EXTENSIONS
More terms from R. J. Mathar, Apr 15 2010
STATUS
approved