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%I #19 Jul 19 2022 22:58:57
%S 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 14,15,16,16,16,16,17,17,18,19,20,20,20,20,21,21,22,23,24,24,24,24,25,
%U 25,26,27,28,28,28,28,29,29,30
%N Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.
%C Formula (13) on p. 6. Abstract: Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras and then the height-assignments for each topological type.
%C The latter problem being solved by a recursive mechanism that generates all height-assignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) error-correcting codes.
%C Conjecture: essentially partial sums of A169675 (verified for n <= 10000). - _Sean A. Irvine_, Jul 19 2022
%H Nathaniel Johnston, <a href="/A140427/b140427.txt">Table of n, a(n) for n = 0..10000</a>
%H 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.
%F a(n) = 0 for 0 <= n < 4, floor((n-4)^2)/4)+1 for n = 4, 5, 6, 7, a(n-8) + 4 for n>7.
%F Empirical 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 := 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 seq(A140427(n),n=0..62); # _Nathaniel Johnston_, Apr 26 2011
%t 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 Table[a[n], {n, 0, 62}] (* _Jean-François Alcover_, Nov 28 2017, from Maple *)
%K easy,nonn
%O 0,7
%A _Jonathan Vos Post_, Jun 18 2008
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