A107350 Number of isogons with a certain property.

1, 4, 34, 346, 3965, 48396, 615966, 8082457, 108545916, 1484716135, 20612084010, 289688970195, 4113620233260, 58930127470164, 850641610106596, 12360278974175769, 180648953113093368, 2653875476976308643, 39167191622334514398, 580439539153823110678, 8633956582855204662785

Offset: 1

Author

N. J. A. Sloane, May 23 2005

Keywords

• nonn
• easy

Comments

This and A060005 appear in the reference as incidental sequences when computing A007219.

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..200
• L. Sallows, M. Gardner, R. K. Guy and D. E. Knuth, Serial isogons of 90 degrees, Math. Mag. 64 (1991), 315-324.

Crossrefs

Cf. A007219, A060005, A292476.

Programs

Maple

A107350 := proc(n) res := 1 ; for i from 0 to 4*n-1 do res := taylor(res*(1+x^(2*i+1)),x=0,8*n^2+1) ; od ; coeftayl(res,x=0,8*n^2)/2 ; end: for n from 1 to 25 do printf("%d, ",A107350(n)) ; od ; # R. J. Mathar, May 08 2007

Mathematica

a[n_] := SeriesCoefficient[Product[x^(2k - 1) + 1/x^(2k - 1), {k, 1, 4n}], {x, 0, 0}]/2;
Table[a[n], {n, 1, 25}] (* Jean-François Alcover, Mar 10 2023 *)

Formula

product[ {1+x^(2i+1)},i=0,1,...,4n-1] = 1+...+2*a(n)*x^(8n^2)+.... (g.f.). - R. J. Mathar, May 08 2007

a(n) = A292476(2*n)/2. - Seiichi Manyama, Sep 18 2017

Extensions

More terms from R. J. Mathar, May 08 2007