A123955 Expansion of g.f.: x^5/( (1-3*x) * (1-2*x) * (1-4*x) * (1-6*x+6*x^2) ).

0, 0, 0, 0, 1, 15, 139, 1029, 6691, 40041, 226435, 1230009, 6487195, 33464145, 169720915, 849504825, 4208146411, 20674387905, 100901918659, 489826044489, 2367517203931, 11402423910801, 54755709794995, 262308279256089

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

Sequence in context: A030056 A225978 A175707 * A027802 A302855 A133716

Adjacent sequences: A123952 A123953 A123954 * A123956 A123957 A123958

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