A143351 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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