A143375 Expansion of x/(1 - x^2 - 2*x^5 - x^8 - x^10 - x^12).

1, 0, 1, 0, 1, 2, 1, 4, 2, 6, 8, 8, 19, 14, 34, 36, 54, 86, 93, 172, 194, 308, 427, 552, 878, 1076, 1675, 2224, 3120, 4546, 5986, 8928, 11933, 17104, 24005, 32928, 47534, 64640, 92523, 128348, 179418, 253994, 350622, 498000, 690790, 971508, 1362840

Offset

1,6

References

Claude Shannon and Warren Weaver, A Mathematical Theory of Communication, University of Illinois Press, Chicago, 1963, pp. 37-38.

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,2,0,0,1,0,1,0,1).

Formula

a(n) = a(n-2) + 2*a(n-5) + a(n-8) + a(n-10) + a(n-12).

Mathematica

Rest@CoefficientList[Series[x/(1-x^2-2x^5-x^8-x^10-x^12), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 2, 1, 4, 2, 6, 8, 8}, 60] (* Harvey P. Dale, Oct 01 2012 *)

Prog

(PARI) my(x='x+O('x^60)); Vec(x/(1-x^2-2*x^5-x^8-x^10-x^12)) \\ G. C. Greubel, Sep 27 2017
(Sage)
def A143375_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x/(1-x^2-2*x^5-x^8-x^10-x^12) ).list()
a=A143375_list(60); a[1:] # G. C. Greubel, Feb 08 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 60);
Coefficients(R!( x/(1-x^2-2*x^5-x^8-x^10-x^12) )); // G. C. Greubel, Feb 08 2021

Crossrefs

Cf. A122762, A143351, A143372, A143373.

Sequence in context: A353132 A205685 A334404 * A339418 A074364 A256610

Adjacent sequences: A143372 A143373 A143374 * A143376 A143377 A143378

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Oct 22 2008

Extensions

More terms from Harvey P. Dale, Oct 01 2012

Edited by G. C. Greubel, Feb 08 2021

Status

approved