

A007228


a(n) = (3/(n+1)) * C(4n,n).
(Formerly M5200)


4



3, 6, 28, 165, 1092, 7752, 57684, 444015, 3506100, 28242984, 231180144, 1917334783, 16077354108, 136074334200, 1160946392760, 9973891723635, 86210635955220, 749191930237608, 6541908910355280, 57369142749576660, 505045163173167760, 4461713825057817120
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OFFSET

0,1


COMMENTS

Perforation patterns for punctured convolutional codes (4,1).
Apparently Begin's paper was presented at a poster session at the conference and was never published.


REFERENCES

G. Begin, On the enumeration of perforation patterns for punctured convolutional codes, Séries Formelles et Combinatoire Algébrique, 4th colloquium, 1519 Juin 1992, Montréal, Université du Québec à Montréal, pp. 110.
N. S. S. Gu, H. Prodinger, S. Wagner, Bijections for a class of labeled plane trees, Eur. J. Combinat. 31 (2010) 720732, doi10.1016/j.ejc.2009.10.007, Theorem 2 at k=3.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=0..21.


FORMULA

a(n) = C(4n,n)/(3n+1) + 2*C(4n+1,n)/(3n+2) + 3*C(4n+2,n)/(3n+3).  Paul Barry, Nov 05 2006
G.f.: g + g^2 + g^3 where g = 1 + x*g^4 is the g.f. of A002293.  Mark van Hoeij, Nov 11 2011
3*(3*n1)*(3*n2)*(n+1)*a(n)  8*(4*n3)*(2*n1)*(4*n1)*a(n1) = 0.  R. J. Mathar, Nov 24 2012


MATHEMATICA

Table[3/(n+1) Binomial[4n, n], {n, 0, 30}] (* Harvey P. Dale, Nov 14 2013 *)


CROSSREFS

Cf. A007226.
Sequence in context: A068133 A220823 A024497 * A326074 A096155 A007452
Adjacent sequences: A007225 A007226 A007227 * A007229 A007230 A007231


KEYWORD

nonn,easy


AUTHOR

Simon Plouffe


EXTENSIONS

Edited by N. J. A. Sloane, Feb 07 2004 following a suggestion of Ralf Stephan
Reedited by N. J. A. Sloane, May 31 2008 following a suggestion of R. J. Mathar


STATUS

approved



