OFFSET
1,6
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (15,-86,234,-300,144).
FORMULA
a(n) = 15*a(n-1) -86*a(n-2) +234*a(n-3) -300*a(n-4) +144*a(n-5).
a(n) = -2^n/8 +3^n/9 -4^n/16 +A094433(n+1)/12. [Mar 28 2010]
MAPLE
seq(coeff(series(x^5/((1-3*x)*(1-2*x)*(1-4*x)*(1-6*x+6*x^2)), x, n+1), x, n), n = 1..30); # G. C. Greubel, Aug 05 2019
MATHEMATICA
M = {{3, -1, 0, 0, 0}, {-1, 3, -1, 0, 0}, {0, -1, 3, -1, 0}, {0, 0, -1, 3, -1}, {0, 0, 0, -1, 3}}; v[1] = {0, 0, 0, 0, 1}; v[n_]:= v[n] = M.v[n-1]; Table[v[n][[1]], {n, 30}]
LinearRecurrence[{15, -86, 234, -300, 144}, {0, 0, 0, 0, 1}, 30] (* G. C. Greubel, Aug 05 2019 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0, 0, 0], Vec(x^5/((1-3*x)*(1-2*x)*(1- 4*x)*(1-6*x+6*x^2)) )) \\ G. C. Greubel, Aug 05 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); [0, 0, 0, 0] cat Coefficients(R!( x^5/((1-3*x)*(1-2*x)*(1-4*x)*(1-6*x+6*x^2)) )); // G. C. Greubel, Aug 05 2019
(Sage) a=(x^5/((1-3*x)*(1-2*x)*(1-4*x)*(1-6*x+6*x^2))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Aug 05 2019
(GAP) a:=[0, 0, 0, 0, 1];; for n in [6..30] do a[n]:=15*a[n-1]-86*a[n-2]+ 234*a[n-3]-300*a[n-4]+144*a[n-5]; od; a; # G. C. Greubel, Aug 05 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson and Roger L. Bagula, Oct 27 2006
EXTENSIONS
G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009
Definition replaced with Voznyy's generating function of Jul 2009 - the Assoc. Eds of the OEIS, Mar 28 2010
STATUS
approved