A143351 Expansion of x/(1 -x^2 -x^4 -x^7 -x^8 -x^9 -x^10).

1, 0, 1, 0, 2, 0, 3, 1, 6, 3, 11, 7, 20, 15, 37, 32, 70, 68, 134, 141, 257, 288, 495, 583, 959, 1175, 1867, 2358, 3646, 4714, 7136, 9397, 13994, 18695, 27489, 37138, 54068, 73687, 106450, 146066, 209740, 289328, 413506, 572784, 815628, 1133455, 1609405

Offset

1,5

References

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

Links

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

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

Formula

a(n) = a(n-2) +a(n-4) +a(n-7) +a(n-8) +a(n-9) +a(n-10).

Mathematica

Rest@CoefficientList[Series[x/(1-x^2-x^4-x^7-x^8-x^9-x^10), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 1, 0, 1, 0, 0, 1, 1, 1, 1}, {1, 0, 1, 0, 2, 0, 3, 1, 6, 3}, 60] (* Harvey P. Dale, Mar 05 2016 *)

Prog

(Sage)
def A143351_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( x/(1-x^2-x^4-x^7-x^8-x^9-x^10) ).list()
a=A143351_list(61); a[1:] # G. C. Greubel, Feb 08 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 60);
Coefficients(R!( x/(1-x^2-x^4-x^7-x^8-x^9-x^10) )); // G. C. Greubel, Feb 08 2021

Crossrefs

Cf. A122762, A143372, A143373, A143375.

Sequence in context: A006209 A005307 A340385 * A350962 A241644 A241640

Adjacent sequences: A143348 A143349 A143350 * A143352 A143353 A143354

Keyword

nonn

Author

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

Extensions

More terms from Harvey P. Dale, Mar 05 2016

Edited by G. C. Greubel, Feb 08 2021

Status

approved