A140426 Number of multi-symmetric Steinhaus matrices of size n.

1, 1, 2, 1, 2, 2, 2, 2, 4, 2, 4, 4, 4, 4, 8, 4, 8, 8, 8, 8, 16, 8, 16, 16, 16, 16, 32, 16, 32, 32, 32, 32, 64, 32, 64, 64, 64, 64, 128, 64, 128, 128, 128, 128, 256, 128, 256, 256, 256, 256, 512, 256, 512, 512, 512, 512, 1024, 512, 1024, 1024, 1024, 1024, 2048, 1024, 2048, 2048, 2048, 2048, 4096, 2048

Offset: 0

Author

Jonathan Vos Post, Jun 18 2008

Keywords

• easy
• nonn

Comments

Theorem 3.7, p. 9, of Chappelon.

Links

• Jonathan Chappelon, Regular Steinhaus graphs of odd degree, arXiv:0806.2779 [math.CO], 2008-2009.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2)

Crossrefs

Cf. A060548.

Programs

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 2}, {1, 1, 2, 1, 2, 2}, 100] (* Jean-François Alcover, Sep 25 2019 *)

PARI

Vec((1 + x + 2*x^2 + x^3 + 2*x^4 + 2*x^5)/(1 - 2*x^6) + O(x^80)) \\ Andrew Howroyd, Nov 03 2018

Formula

a(n) = 2^ceiling(n/6) for n even, 2^ceiling((n-3)/6) for n odd.

G.f.: ( -1-x-2*x^2-x^3-2*x^4-2*x^5 ) / ( -1+2*x^6 ). - R. J. Mathar, Jan 22 2011

a(n) = A060548(n-1) for n >= 2. - Georg Fischer, Nov 03 2018