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

1,2

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.

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

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 *)

Crossrefs

Cf. A007219, A060005, A292476.

Sequence in context: A333095 A214693 A371379 * A206180 A274344 A199752

Adjacent sequences: A107347 A107348 A107349 * A107351 A107352 A107353

Keyword

nonn,easy

Author

N. J. A. Sloane, May 23 2005

Extensions

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

Status

approved