A138495 First differences of A138477.
0, 1, 1, 1, 3, 9, 15, 25, 55, 121, 231, 441, 903, 1849, 3655, 7225, 14535, 29241, 58311, 116281, 232903, 466489, 932295, 1863225, 3727815, 7458361, 14913991, 29822521, 59650503, 119311929, 238612935, 477204025, 954429895, 1908903481, 3817763271, 7635439161, 15270965703
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (1, 0, 2, 4).
Crossrefs
Cf. A138477.
Programs
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GAP
a:=[0,1,1,1];; for n in [5..40] do a[n]:=a[n-1]+2*a[n-3]+4*a[n-4]; od; a; # G. C. Greubel, May 24 2019
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Magma
R
:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x/((1-2*x)*(1+x)*(1+2*x^2)) )); // G. C. Greubel, May 24 2019 -
Mathematica
LinearRecurrence[{1,0,2,4}, {0,1,1,1}, 40] (* G. C. Greubel, May 24 2019 *) -
PARI
concat(0, Vec(x/((1-2*x)*(1+x)*(1+2*x^2)) + O(x^40))) \\ Michel Marcus, May 24 2019
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Sage
(x/((1-2*x)*(1+x)*(1+2*x^2))).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, May 24 2019
Formula
From R. J. Mathar, May 19 2008: (Start)
O.g.f.: x/((1-2*x)*(1+x)*(1+2*x^2)).
a(n) = a(n-1) + 2*a(n-3) + 4*a(n-4). (End)
E.g.f.: (2*exp(2*x) - exp(-x) - cos(sqrt(2)*x) + 2*sqrt(2)*sin(sqrt(2)*x) )/9. - G. C. Greubel, May 24 2019
Extensions
a(13) corrected by Georg Fischer, May 24 2019
More terms from Michel Marcus, May 24 2019