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A143375
Expansion of x/(1 - x^2 - 2*x^5 - x^8 - x^10 - x^12).
5
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.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Harvey P. Dale, Oct 01 2012
Edited by G. C. Greubel, Feb 08 2021
STATUS
approved