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

Author

Gary W. Adamson and Roger L. Bagula, Oct 27 2006

Keywords

• nonn
• easy

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).

Programs

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

Magma

R:=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

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 *)

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

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

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]

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