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A192905 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments. 3
0, 1, 3, 8, 25, 79, 248, 777, 2435, 7632, 23921, 74975, 234992, 736529, 2308483, 7235416, 22677769, 71078319, 222778856, 698249753, 2188505347, 6859373216, 21499148257, 67384199871, 211200478176, 661959956001, 2074763216131 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The titular polynomial is defined by p(n,x) = (x^2)*p(n-1,x) + x*p(n-2,x), with p(0,x) = 1, p(1,x) = x.  For details, see A192904.

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).

FORMULA

a(n) = 3*a(n-1) + a(n-3) + a(n-4).

G.f.: x*(1-x)*(1+x)/(1-3*x-x^3-x^4). - Colin Barker, Aug 31 2012

MATHEMATICA

(See A192904.)

LinearRecurrence[{3, 0, 1, 1}, {0, 1, 3, 8}, 30] (* G. C. Greubel, Jan 11 2019 *)

PROG

(PARI) my(x='x+O('x^30)); concat([0], Vec(x*(1-x^2)/(1-3*x-x^3-x^4))) \\ G. C. Greubel, Jan 11 2019

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-x^2)/(1-3*x-x^3-x^4) )); // G. C. Greubel, Jan 11 2019

(Sage) (x*(1-x^2)/(1-3*x-x^3-x^4)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 11 2019

(GAP) a:=[0, 1, 3, 8];; 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

CROSSREFS

Cf. A192232, A192744, A192904, A192872.

Sequence in context: A007563 A050383 A060404 * A192207 A289593 A101490

Adjacent sequences:  A192902 A192903 A192904 * A192906 A192907 A192908

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Jul 12 2011

STATUS

approved

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Last modified October 21 13:19 EDT 2021. Contains 348155 sequences. (Running on oeis4.)