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

%I A140427 #26 Sep 30 2024 04:50:48
%S A140427 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,
%T A140427 14,15,16,16,16,16,17,17,18,19,20,20,20,20,21,21,22,23,24,24,24,24,25,
%U A140427 25,26,27,28,28,28,28,29,29,30
%N A140427 Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.
%C A140427 Conjecture: essentially partial sums of A169675 (verified for n <= 10000). - _Sean A. Irvine_, Jul 19 2022
%H A140427 Nathaniel Johnston, <a href="/A140427/b140427.txt">Table of n, a(n) for n = 0..10000</a>
%H A140427 C. F. Doran, M. G. Faux, S. J. Gates Jr, T. Hubsch, K. M. Iga and G. D. Landweber, <a href="http://arxiv.org/abs/0806.0051">Relating Doubly-Even Error-Correcting Codes, Graphs and Irreducible Representations of N-Extended Supersymmetry</a>, arXiv:0806.0051 [hep-th], 2008. See formula (13) on page 6.
%F A140427 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.
%F A140427 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
%p A140427 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:
%p A140427 seq(A140427(n),n=0..62); # _Nathaniel Johnston_, Apr 26 2011
%t A140427 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]]];
%t A140427 Table[a[n], {n, 0, 62}] (* _Jean-François Alcover_, Nov 28 2017, from Maple *)
%K A140427 easy,nonn
%O A140427 0,7
%A A140427 _Jonathan Vos Post_, Jun 18 2008