A108095 Coefficients of series whose square is the weight enumerator of the [8,4,4] Hamming code (see A002337).

1, 7, -24, 168, -1464, 14280, -149208, 1633128, -18483576, 214552968, -2540241816, 30557794344, -372427799352, 4588869057864, -57068241380952, 715388746153704, -9030126770703096, 114677768635083528, -1464172925174652696, 18783553808927819688, -242002474839216810168

Offset

0,2

Links

Table of n, a(n) for n=0..20.

N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

G. Levy, Solution of second order recurrence equations (2010) PhD Thesis, Florida State University, page 2

Formula

G.f.: sqrt(1+14*x^4+x^8).

D-finite with recurrence: n*a(n) +7*(2*n-3)*a(n-1) +(n-3)*a(n-2)=0. - R. J. Mathar, Jan 09 2020

Example

More precisely, the Hamming code has weight enumerator 1 + 14*x^4 + x^8 and the square root of this is 1 + 7*x^4 - 24*x^8 + 168*x^12 - 1464*x^16 + 14280*x^20 - 149208*x^24 + ...

Mathematica

a = DifferenceRoot[Function[{a, n}, {(n-1)a[n] + 7(2n+1)a[n+1] + (n+2)a[n+2] == 0, a[0] == 1, a[1] == 7}]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Dec 17 2018 *)

Crossrefs

Cf. A002337, A002393.

Sequence in context: A007750 A153577 A009643 * A223007 A009646 A293489

Adjacent sequences: A108092 A108093 A108094 * A108096 A108097 A108098

Keyword

sign,easy

Author

N. J. A. Sloane and Michael Somos, Jun 06 2005

Status

approved