A192907 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments.
0, 1, 4, 12, 37, 116, 364, 1141, 3576, 11208, 35129, 110104, 345096, 1081625, 3390108, 10625524, 33303293, 104381612, 327160468, 1025410221, 3213915568, 10073288784, 31572437041, 98956636912
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 (3,0,1,1).
Crossrefs
Cf. A192906.
Programs
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GAP
a:=[0,1,4,12];; for n in [5..30] do a[n]:=3*a[n-1]+a[n-3]+a[n-4]; od; a; # G. C. Greubel, Jan 11 2019
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Magma
m:=30; R
:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1+x)/(1-3*x-x^3-x^4) )); // G. C. Greubel, Jan 11 2019 -
Mathematica
(See A192906.) LinearRecurrence[{3,0,1,1}, {0,1,4,12}, 30] (* G. C. Greubel, Jan 11 2019 *)
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PARI
my(x='x+O('x^30)); concat([0], Vec(x*(1+x)/(1-3*x-x^3-x^4))) \\ G. C. Greubel, Jan 11 2019 -
Sage
(x*(1+x)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 11 2019
Formula
a(n) = 3*a(n-1) + a(n-3) + a(n-4).
G.f. x*(1+x)/( 1-3*x-x^3-x^4 ). - R. J. Mathar, Jul 13 2011
Comments