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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 (list; graph; refs; listen; history; text; internal format)
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, 15-19 Juin 1992, Montréal, Université du Québec à Montréal, pp. 1-10.

N. S. S. Gu, H. Prodinger, S. Wagner, Bijections for a class of labeled plane trees, Eur. J. Combinat. 31 (2010) 720-732, doi|10.1016/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*n-1)*(3*n-2)*(n+1)*a(n) - 8*(4*n-3)*(2*n-1)*(4*n-1)*a(n-1) = 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 * A096155 A007452 A046981

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

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Last modified March 19 19:32 EDT 2019. Contains 321330 sequences. (Running on oeis4.)