OFFSET
0,2
REFERENCES
A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-14,15,-5,-4,4,-1)
FORMULA
a(n) = 3*F(n+10) + F(n+9) - (3*n^4 + 58*n^3 + 489*n^2 + 2234*n + 4752)/24, where F(.) are the Fibonacci numbers (A000045).
a(n) = a(n-1) + a(n-2) + (3*n+4)*C(n+3, 3)/4.
G.f.: (1 + 2*x)/((1 - x - x^2)*(1 - x)^5). - R. J. Mathar, Nov 28 2008
MATHEMATICA
LinearRecurrence[{6, -14, 15, -5, -4, 4, -1}, {1, 8, 34, 107, 281, 654, 1397}, 30] (* Harvey P. Dale, May 09 2018 *)
CoefficientList[Series[(1+2x)/((1-x-x^2)(1-x)^5), {x, 0, 50}], x] (* G. C. Greubel, May 24 2018 *)
PROG
(PARI) x='x+O('x^30); Vec((1+2*x)/((1-x-x^2)*(1-x)^5)) \\ G. C. Greubel, May 24 2018
(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+2*x)/((1-x-x^2)*(1-x)^5))); // G. C. Greubel, May 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Barry E. Williams, Mar 04 2000
STATUS
approved