

A140427


Arises in relating doublyeven errorcorrecting codes, graphs and irreducible representations of Nextended supersymmetry.


1



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
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OFFSET

0,7


COMMENTS

Formula (13) on p. 6. Abstract: Previous work has shown that the classification of indecomposable offshell representations of Nsupersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras and then the heightassignments for each topological type.
The latter problem being solved by a recursive mechanism that generates all heightassignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) errorcorrecting codes.


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 DoublyEven ErrorCorrecting Codes, Graphs and Irreducible Representations of NExtended Supersymmetry, arXiv:0806.0051 [hepth], 2008.


FORMULA

a(n) = 0 for 0 <= n < 4, floor((n4)^2)/4)+1 for n = 4, 5, 6, 7, a(n8) + 4 for n>7.
Empirical g.f.: x^4*(x^4+x^3+x^2+1) / ((x1)^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}] (* JeanFrançois 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



