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 A145840 Number of 4-compositions of n. 5
 1, 4, 26, 164, 1031, 6480, 40728, 255984, 1608914, 10112368, 63558392, 399478064, 2510804924, 15780945024, 99186608832, 623409013632, 3918258753416, 24627092844352, 154786536605216, 972866430709568, 6114673231661936, 38432026791933696, 241553493927992448 (list; graph; refs; listen; history; text; internal format)
 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 Alois P. Heinz, Table of n, a(n) for n = 0..1000 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 Index entries for linear recurrences with constant coefficients, signature (8,-12,8,-2). 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 Cf. A003480, A145839, A145841. Column k=4 of A261780. Sequence in context: A121767 A092167 A124544 * A302335 A244787 A220305 Adjacent sequences:  A145837 A145838 A145839 * A145841 A145842 A145843 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

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Last modified June 22 13:46 EDT 2021. Contains 345380 sequences. (Running on oeis4.)