login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A192907 Coefficient of x in the reduction by (x^2 -> x + 1) of the polynomial p(n,x) defined below at Comments. 3
0, 1, 4, 12, 37, 116, 364, 1141, 3576, 11208, 35129, 110104, 345096, 1081625, 3390108, 10625524, 33303293, 104381612, 327160468, 1025410221, 3213915568, 10073288784, 31572437041, 98956636912 (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 + 1.

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)/( 1-3*x-x^3-x^4 ). - R. J. Mathar, Jul 13 2011

MATHEMATICA

(See A192906.)

LinearRecurrence[{3, 0, 1, 1}, {0, 1, 4, 12}, 30] (* G. C. Greubel, Jan 11 2019 *)

PROG

(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

(MAGMA) m:=30; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( 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

(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

CROSSREFS

Cf. A192906.

Sequence in context: A099098 A019481 A019480 * A280891 A149319 A149320

Adjacent sequences:  A192904 A192905 A192906 * A192908 A192909 A192910

KEYWORD

nonn

AUTHOR

Clark Kimberling, Jul 12 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 13:20 EDT 2020. Contains 334683 sequences. (Running on oeis4.)