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A140427 Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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.

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.

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.

FORMULA

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.

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

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-Fran├žois 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

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)