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A145840
Number of 4-compositions of n.
6
1, 4, 26, 164, 1031, 6480, 40728, 255984, 1608914, 10112368, 63558392, 399478064, 2510804924, 15780945024, 99186608832, 623409013632, 3918258753416, 24627092844352, 154786536605216, 972866430709568, 6114673231661936, 38432026791933696, 241553493927992448
OFFSET
0,2
COMMENTS
A 4-composition of n is a matrix with four rows, such that each column has at least one nonzero element and whose elements sum up to n.
REFERENCES
G. Louchard, Matrix compositions: a probabilistic approach, Proceedings of GASCom and Bijective Combinatorics 2008, Bibbiena, Italy, pp. 159-170.
E. Munarini, M. Poneti and S. Rinaldi, Matrix compositions, Proceedings of Formal Power Series and Algebraic Combinatorics 2006, San Diego, USA, J. Remmel, M. Zabrocki (Editors) 445-456.
LINKS
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
E. Munarini, M. Poneti, S. Rimaldi, Matrix compositions, JIS 12 (2009) 09.4.8
FORMULA
a(n+4) = 8*a(n+3)-12*a(n+2)+8*a(n+1)-2*a(n).
G.f.: (1-x)^4/(2*(1-x)^4-1).
a(n) = sum(k>=0, C(n+4*k-1,n) / 2^(k+1)). - Vaclav Kotesovec, Dec 31 2013
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+3, 3), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Sep 01 2015
MATHEMATICA
Table[Sum[Binomial[n+4*k-1, n]/2^(k+1), {k, 0, Infinity}], {n, 0, 20}] (* Vaclav Kotesovec, Dec 31 2013 *)
CROSSREFS
Column k=4 of A261780.
Sequence in context: A121767 A092167 A124544 * A302335 A244787 A220305
KEYWORD
nonn,easy
AUTHOR
Simone Rinaldi (rinaldi(AT)unisi.it), Oct 21 2008
EXTENSIONS
Offset corrected by Alois P. Heinz, Aug 31 2015
STATUS
approved