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

0,7

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.

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

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 *)

Crossrefs

Sequence in context: A287635 A189660 A194167 * A194816 A178770 A072229

Adjacent sequences: A140424 A140425 A140426 * A140428 A140429 A140430

Keyword

easy,nonn

Author

Jonathan Vos Post, Jun 18 2008

Status

approved