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URL: https://oeis.org/A161434

⇱ A161434 - OEIS

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A161434
Number of 6-compositions.
2
1, 6, 57, 524, 4803, 44022, 403495, 3698352, 33898338, 310705224, 2847860436, 26102905368, 239253883390, 2192952083712, 20100149570496, 184233853423936, 1688649759962676, 15477817777932456, 141866507103389516, 1300319342589168000, 11918460722228694720
OFFSET
0,2
COMMENTS
Excluding the terms of A161434(0) followed by the INVERTi transform yields A000389 without A000389(0). - Alexander R. Povolotsky and R. J. Mathar, Jun 16 2009
LINKS
E. Grazzini, E. Munarini, M. Poneti, S. Rinaldi, m-compositions and m-partitions: exhaustive generation and Gray code, Pure Math. Appl. 17 (2006), 111-121.
M. Janjic, On Linear Recurrence Equations Arising from Compositions of Positive Integers, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.7.
G. Louchard, Matrix Compositions: a Probabilistic analysis, Proc. GASCOM'08, Pure Mathematics and Applications, 19, 2-3, 127-146, 2008.
E. Munarini, M. Poneti, S. Rinaldi, Matrix compositions, Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.8
FORMULA
Recurrence: a(n+6) = 12*a(n+5) - 30*a(n+4) + 40*a(n+3) - 30*a(n+2) + 12*a(n+1) - 2*a(n).
G.f.: (1-x)^6/(2*(1-x)^6-1).
a(n) = Sum_{k>=0} (1/2)^(k+1) * binomial(n-1+6*k,n). - Seiichi Manyama, Aug 06 2024
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
add(a(n-j)*binomial(j+5, 5), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Sep 01 2015
MATHEMATICA
Join[{1}, LinearRecurrence[{12, -30, 40, -30, 12, -2}, {6, 57, 524, 4803, 44022, 403495}, 20]] (* Jean-François Alcover, Jan 08 2016 *)
CoefficientList[Series[(1-x)^6/(2*(1-x)^6-1), {x, 0, 50}], x] (* G. C. Greubel, Nov 25 2017 *)
PROG
(PARI) x='x+O('x^30); Vec((1-x)^6/(2*(1-x)^6-1)) \\ G. C. Greubel, Nov 25 2017
CROSSREFS
Column k=6 of A261780.
Sequence in context: A124546 A144070 A095900 * A332620 A390332 A386938
KEYWORD
nonn,easy
AUTHOR
Emanuele Munarini, Jun 10 2009
STATUS
approved