

A105423


Number of compositions of n+2 having exactly two parts equal to 1.


8



1, 0, 3, 3, 9, 15, 31, 57, 108, 199, 366, 666, 1205, 2166, 3873, 6891, 12207, 21537, 37859, 66327, 115842, 201743, 350412, 607140, 1049545, 1810428, 3116655, 5355219, 9185349, 15728547, 26890375, 45904773, 78253896, 133221079
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OFFSET

0,3


COMMENTS



LINKS



FORMULA

G.f.: (1z)^3/(1zz^2)^3.
a(n) = (1/50) [(5n^2+21n+25)*Lucas(n)  (11n^2+30n+10)*Fibonacci(n) ].  Ralf Stephan, Jun 01 2007


EXAMPLE

a(4)=9 because we have (1,1,4),(1,4,1),(4,1,1),(1,1,2,2),(1,2,1,2),(1,2,2,1),(2,1,1,2),(2,1,2,1) and (2,2,1,1).


MAPLE

G:=(1z)^3/(1zz^2)^3: Gser:=series(G, z=0, 42): 1, seq(coeff(Gser, z^n), n=1..40);


MATHEMATICA

LinearRecurrence[{3, 0, 5, 0, 3, 1}, {1, 0, 3, 3, 9, 15}, 40] (* JeanFrançois Alcover, Jul 23 2018 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



