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A105423
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Number of compositions of n+2 having exactly two parts equal to 1.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Column 2 of A105422.
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FORMULA
| G.f.=(1-z)^3/(1-z-z^2)^3.
(1/50) [(5n^2+21n+25)*Lucas(n) - (11n^2+30n+10)*Fibonacci(n) ]. - Ralf Stephan, Jun 1 2007
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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).
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MAPLE
| G:=(1-z)^3/(1-z-z^2)^3: Gser:=series(G, z=0, 42): 1, seq(coeff(Gser, z^n), n=1..40);
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CROSSREFS
| Cf. A105422.
Sequence in context: A052436 A122847 A197462 * A147471 A062510 A000200
Adjacent sequences: A105420 A105421 A105422 * A105424 A105425 A105426
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Apr 07 2005
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