OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., pp. 189, 194-196.
J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 224.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
FORMULA
a(n) = a(n-1) + a(n-2) + 4; a(0)=1, a(1)=5; n >= 1.
a(n) = 4*F(n+2) + F(n+1) - 4, where F(k) is A000045(k).
From R. J. Mathar, Apr 29 2013: (Start)
G.f.: ( 1+3*x ) / ( (x-1)*(x^2+x-1) ).
MATHEMATICA
CoefficientList[Series[(1+3*x)/((x-1)*(x^2+x-1)), {x, 0, 50}], x] (* G. C. Greubel, May 24 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1+3*x)/((x-1)*(x^2+x-1))) \\ G. C. Greubel, May 24 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+3*x)/((x-1)*(x^2+x-1)))); // G. C. Greubel, May 24 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Mar 06 2000
STATUS
approved