The OEIS is supported by the many generous donors to the OEIS Foundation.

A192813
Coefficient of x in the reduction of the polynomial x^(2*n) + x^n + 1 by x^3 -> x + 1.
2
0, 1, 1, 3, 4, 6, 11, 18, 31, 53, 91, 158, 274, 477, 832, 1453, 2541, 4447, 7788, 13646, 23919, 41938, 73547, 129001, 226295, 397006, 696546, 1222153, 2144464, 3762921, 6603001, 11586843, 20332676, 35680278, 62613091, 109876418, 192817159
OFFSET
1,4
For discussions of polynomial reduction, see A192232 and A192744.
FORMULA
a(n) = 2*a(n-1) - a(n-4) - a(n-6).
G.f.: -x^2*(x^4+2*x^3-x^2+x-1)/((x^3-x^2+2*x-1)*(x^3+x^2-1)). - Colin Barker, Nov 23 2012
MAPLE
seq(coeff(series((-x^2*(x^4+2*x^3-x^2+x-1))/((x^3-x^2+2*x-1)*(x^3+x^2-1)), x, n+1), x, n), n = 1 .. 40); # Muniru A Asiru, Jan 03 2019
MATHEMATICA
(See A192812.)
LinearRecurrence[{2, 0, 0, -1, 0, -1}, {0, 1, 1, 3, 4, 6}, 40] (* G. C. Greubel, Jan 03 2019 *)
PROG
(PARI) my(x='x+O('x^40)); concat([0], Vec(x^2*(1-x+x^2-2*x^3-x^4)/((1-x^2-x^3)*(1-2*x+x^2-x^3)))) \\ G. C. Greubel, Jan 03 2019
(Magma) m:=40; R<x>:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x^2*(1-x+x^2-2*x^3-x^4)/((1-x^2-x^3)*(1-2*x+x^2-x^3)) )); // G. C. Greubel, Jan 03 2019
(Sage) a=(x^2*(1-x+x^2-2*x^3-x^4)/((1-x^2-x^3)*(1-2*x+x^2-x^3)) ).series(x, 40).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jan 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 10 2011
STATUS
approved

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

Last modified September 20 03:37 EDT 2024. Contains 376016 sequences. (Running on oeis4.)