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A007228 a(n) = (3/(n+1)) * C(4n,n).
(Formerly M5200)
4

%I M5200

%S 3,6,28,165,1092,7752,57684,444015,3506100,28242984,231180144,

%T 1917334783,16077354108,136074334200,1160946392760,9973891723635,

%U 86210635955220,749191930237608,6541908910355280,57369142749576660,505045163173167760,4461713825057817120

%N a(n) = (3/(n+1)) * C(4n,n).

%C Perforation patterns for punctured convolutional codes (4,1).

%C Apparently Begin's paper was presented at a poster session at the conference and was never published.

%D 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.

%D 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.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%F 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

%F 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

%F 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

%t Table[3/(n+1) Binomial[4n,n],{n,0,30}] (* _Harvey P. Dale_, Nov 14 2013 *)

%Y Cf. A007226.

%K nonn,easy

%O 0,1

%A _Simon Plouffe_

%E Edited by _N. J. A. Sloane_, Feb 07 2004 following a suggestion of _Ralf Stephan_

%E Reedited by _N. J. A. Sloane_, May 31 2008 following a suggestion of _R. J. Mathar_

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)