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A145839
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Number of 3-compositions of n
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0
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1, 3, 15, 73, 354, 1716, 8318, 40320, 195444, 947380, 4592256, 22260144, 107902088, 523036176, 2535324816, 12289536016, 59571339552, 288761470848, 1399719859808, 6784893012864
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A 3-composition of n is a matrix with three rows, such that each column has at least one non zero element and whose elements sum up to n
Matrix inverse of (A000217(A004736)*A154990). [From Mats Granvik (mats.granvik(AT)abo.fi), Jan 19 2009]
(1 + 3x + 15x^2 + 73x^3 + ...) = 1/(1-3x-6x^2-10x^3-15x^4 - ...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 27 2009]
For n>1, a(n) is the number of generalized compositions of n-1 when there are i^2/2+3i/2+1 different types of i, (i=1,2,...). [From Milan R. Janjic (agnus(AT)blic.net), Sep 24 2010]
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REFERENCES
| G. Louchard, Matrix compositions: a probabilistic approach, Proceedings of GASCom and Bijective Combinatorics 2008, Bibbiena, Italy, p. 159-170.
E. Munarini, M. Poneti and S. Rinaldi, Matrix compositions, (preprint)
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FORMULA
| a(n+3)=6a(n+2)-6a(n+1)+2a(n); G.f.: (1-x)^3/(2(1-x)^3-1)
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CROSSREFS
| Cf. A003480, 2-compositions
Sequence in context: A155117 A137638 A156019 * A055837 A124543 A007142
Adjacent sequences: A145836 A145837 A145838 * A145840 A145841 A145842
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KEYWORD
| nonn
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AUTHOR
| Simone Rinaldi (rinaldi(AT)unisi.it), Oct 21 2008
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