%I A055991
%S A055991 1,5,19,69,250,907,3292,11949,43371,157422,571388,2073943,7527704,
%T A055991 27322992,99173120,359964521,1306548149,4742323107,17213011605,
%U A055991 62477347458,226771411939,823102698260,2987581397893,10843899100203
%N A055991 a(n) is its own 4th difference.
%C A055991 a(n) = number of unique matrix products in (A+B+C+D+E)^n where A,B,C 
               and D all commute with each other, but not with E. - Paul D. Hanna 
               and Max Alekseyev (maxale(AT)gmail.com), Feb 01 2006
%C A055991 Row sums of Riordan array (1,1/(1-x)^4). - Paul Barry (pbarry(AT)wit.ie), 
               Feb 02 2006
%C A055991 Quadrisection of A003269: a(n)=A003269(4n-1); - Paul Barry (pbarry(AT)wit.ie), 
               Feb 02 2006
%C A055991 Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 23 2009: 
               (Start)
%C A055991 Equals the INVERT transform of the tetrahedral series.
%C A055991 a(4) = 69 = (1, 4, 10) dot (19, 5, 1) + 20; = (19 + 20 + 10) + 20. (End)
%F A055991 a(n) = 5a(n-1)-6a(n-2)+4a(n-3)-a(n-4) = a(n-1)+A055990(n) = A055988(n+1)-A055988(n) 
               = A055989(n+1)-2*A055989(n)+A055989(n-1).
%F A055991 Letting a(0)=1, we have a(n)=sum(u=0, n-1, sum(v=0, u, sum(w=0, v, sum(x=0, 
               w, a(x))))) for n>0. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 26 2003
%F A055991 a(n) = Sum_{k=1..n} binomial(n+3*k-1, n-k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 23 2003
%F A055991 a(n)=sum{k=0..n, binomial(4n-3k-1,k)}; - Paul Barry (pbarry(AT)wit.ie), 
               Feb 02 2006
%F A055991 G.f.: (1-x)^4/(1-5x+6x^2-4x^3+x^4); - Paul Barry (pbarry(AT)wit.ie), 
               Feb 02 2006
%Y A055991 Cf. A055988, A055989, A055990 for the other differences of a(n). See 
               A000079, A001906, A052529 for examples of sequences which are respectively 
               their own first, second and third differences.
%Y A055991 Sequence in context: A070857 A143954 A047145 this_sequence A030662 A149758 
               A026590
%Y A055991 Adjacent sequences: A055988 A055989 A055990 this_sequence A055992 A055993 
               A055994
%K A055991 nonn
%O A055991 1,2
%A A055991 Henry Bottomley (se16(AT)btinternet.com), Jun 02 2000
%E A055991 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 05 2000