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A130567 The number of involutions for group G_n for a(0)=2 instead of 1 or 5: G_n+1=G_n(Central Product) D_8. 0
2, 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023, 70368760954879 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(0)=1->A099393 a(0)=3 minus a(n)-3^(n+1)-> A028244

REFERENCES

A.M.Cohen and D.E. Taylor, American Math Monthly, volume 114,Number 7, Aug-Sept 2007, pages 633-638

LINKS

Table of n, a(n) for n=1..24.

FORMULA

a(n) = 2^(2*n - 1) + 2*a(n - 1) + 1

O.g.f.: x(2-7x+2x^2)/((1-x)(1-4x)(1-2x)). a(n)=A093069(n-2), n>1. - R. J. Mathar, Jun 13 2008

a(n)=-1+2*2^n+4^n, with n>=0 - Paolo P. Lava, Jul 30 2008

MATHEMATICA

f[n_Integer?Positive] := f[n] = 2^(2*n - 1) + 2*f[n - 1] + 1; f[0] = 2; Table[f[n], {n, 0, 30}]

CROSSREFS

Cf. A099393, A028244.

Sequence in context: A198944 A112657 A007717 * A091514 A143629 A176287

Adjacent sequences:  A130564 A130565 A130566 * A130568 A130569 A130570

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Aug 09 2007

STATUS

approved

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Last modified November 27 20:25 EST 2014. Contains 250271 sequences.