A122762 a(n) = a(n-2) + a(n-4) + a(n-5) + a(n-7) + a(n-8) + a(n-10) for n >= 10, with a(0) = ... = a(9) = 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 6, 11, 11, 21, 26, 41, 56, 86, 121, 181, 256, 381, 541, 801, 1146, 1686, 2426, 3551, 5131, 7486, 10841, 15791, 22896, 33321, 48346, 70321, 102076, 148416, 215506, 313256, 454961, 661206, 960446, 1395686, 2027501

Offset

0,11

Comments

Shannon mentions this recurrence with characteristic polynomial x^10 +x^8 +x^7 +x^5 +x^4 +x^2 -1 = 0 in connection with the channel capacity Cp = Log[W] = Log[xroot_max] = 0.539... .

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 = 0..1000

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

Formula

O.g.f.: (1 +x -x^4 -2*x^5 -2*x^6 -3*x^7 -4*x^8 -4*x^9)/(1 -x^2 -x^4 -x^5 -x^7 -x^8 -x^10). - R. J. Mathar, Dec 05 2007

Mathematica

a[n_]:= a[n]= If[n<10, 1, a[n-2] +a[n-4] +a[n-5] +a[n-7] +a[n-8] +a[n-10]];
Table[a[n], {n, 0, 50}]

Prog

(Sage)
def A122762_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x-x^4-2*x^5-2*x^6-3*x^7-4*x^8-4*x^9)/(1-x^2-x^4-x^5-x^7-x^8 -x^10) ).list()
A122762_list(50) # G. C. Greubel, Feb 08 2021
(Magma)
R<x>:=PowerSeriesRing(Rationals(), 50);
Coefficients(R!( (1+x-x^4-2*x^5-2*x^6-3*x^7-4*x^8-4*x^9)/(1-x^2-x^4-x^5-x^7-x^8 -x^10) )); // G. C. Greubel, Feb 08 2021

Crossrefs

Cf. A143351, A143372, A143373, A143375.

Sequence in context: A240620 A344328 A168282 * A046605 A095899 A346530

Adjacent sequences: A122759 A122760 A122761 * A122763 A122764 A122765

Keyword

nonn

Author

Roger L. Bagula, Sep 21 2006

Extensions

Edited by N. J. A. Sloane, May 09 2007

Status

approved