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Search: id:A052529
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| A052529 |
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A simple regular expression. |
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+0
9
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| 1, 1, 4, 13, 41, 129, 406, 1278, 4023, 12664, 39865, 125491, 395033, 1243524, 3914488, 12322413, 38789712, 122106097, 384377665, 1209982081, 3808901426, 11990037126, 37743426307, 118812495276, 374009739309, 1177344897715
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Sum[a=0..n, Sum[b=0..n, Sum[c=0..n, C(n-b-c,a)*C(n-a-c,b)*C(n-a-b,c) ]]].
a(n+1) = number of unique matrix products in (A+B+C+D)^n where commutator [A,B]=[A,D]=[B,D]=0 but D does not commute with A, B, or C. - Paul D. Hanna and Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 01 2006
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REFERENCES
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A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, id. 80.
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 459
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FORMULA
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G.f.: (-1+x)^3/(-1+4*x-3*x^2+x^3)
Recurrence: a(n)=4*a(n-1)-3*a(n-2)+a(n-3) for n>=4.
Sum(-1/31*(5*_alpha+3*_alpha^2-6)*_alpha^(-1-n), _alpha=RootOf(-1+4*_Z-3*_Z^2+_Z^3))
For n>0, a(n)=sum(k=0, n-1, sum(i=0, k, sum(j=0, i, a(j)))). - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 26 2003
a(n) = Sum_{k=0..n} binomial(n+2*k-1, n-k). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Mar 23 2003
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MAPLE
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spec := [S, {S=Sequence(Prod(Z, Sequence(Z), Sequence(Z), Sequence(Z)))}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
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CROSSREFS
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Cf. A001906, A055991.
Trisection of A000930. First differences of A052544.
Sequence in context: A097112 A077284 A070428 this_sequence A049222 A001453 A005002
Adjacent sequences: A052526 A052527 A052528 this_sequence A052530 A052531 A052532
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 08 2000
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