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