A140427 Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.

0, 0, 0, 0, 1, 1, 2, 3, 4, 4, 4, 4, 5, 5, 6, 7, 8, 8, 8, 8, 9, 9, 10, 11, 12, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 16, 17, 17, 18, 19, 20, 20, 20, 20, 21, 21, 22, 23, 24, 24, 24, 24, 25, 25, 26, 27, 28, 28, 28, 28, 29, 29, 30

Offset: 0

Author

Jonathan Vos Post, Jun 18 2008

Keywords

• easy
• nonn

Comments

Conjecture: essentially partial sums of A169675 (verified for n <= 10000). - Sean A. Irvine, Jul 19 2022

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..10000
• C. F. Doran, M. G. Faux, S. J. Gates Jr, T. Hubsch, K. M. Iga and G. D. Landweber, Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry, arXiv:0806.0051 [hep-th], 2008. See formula (13) on page 6.

Programs

Maple

A140427 := proc(n) local l: l:=[0, 0, 0, 0, 1, 1, 2, 3]: if(n<=7)then return l[n+1]:else return l[(n mod 8) + 1] + 4*floor(n/8): fi: end:
seq(A140427(n),n=0..62); # Nathaniel Johnston, Apr 26 2011

Mathematica

a[n_] := Module[{L = {0, 0, 0, 0, 1, 1, 2, 3}}, If[n <= 7, L[[n + 1]], L[[Mod[n, 8] + 1]] + 4*Floor[n/8]]];
Table[a[n], {n, 0, 62}] (* Jean-François Alcover, Nov 28 2017, from Maple *)

Formula

a(n) = 0 for 0 <= n < 4, a(n) = floor(((n-4)^2)/4)+1 for n = 4, 5, 6, 7, and a(n) = a(n-8) + 4 for n>7.

G.f.: x^4*(x^4+x^3+x^2+1) / ((x-1)^2*(x+1)*(x^2+1)*(x^4+1)). - Colin Barker, May 04 2013