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A131661 Number of compositions of n such that the cardinality of the set of parts is 2. 4
0, 0, 2, 5, 14, 22, 44, 68, 107, 172, 261, 396, 606, 950, 1414, 2238, 3418, 5411, 8368, 13297, 20840, 33268, 52549, 84120, 133775, 214611, 343025, 551064, 883600, 1421767, 2284870, 3680296, 5924725, 9551161, 15393855, 24834827, 40061700 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
G.f.: Sum(Sum(x^(i+j)*(x^i+x^j-2)/((x^i-1)*(x^j-1)*(x^i+x^j-1)), j=1..i-1), i=2..infinity).
a(n) ~ 1/sqrt(5) * ((1+sqrt(5))/2)^(n+1). - Vaclav Kotesovec, May 01 2014
MAPLE
with(numtheory):
a:= n-> add(add(add(binomial(j+(n-i*j)/d, j), d=select(x->x<i,
divisors(n-i*j))), j=1..n/i), i=2..n-1):
seq(a(n), n=0..50); # Alois P. Heinz, Feb 01 2014
MATHEMATICA
Rest@ CoefficientList[ Series[ Sum[ x^(i + j)*(x^i + x^j - 2)/((x^i - 1)*(x^j - 1)*(x^i + x^j - 1)), {i, 2, 37}, {j, i - 1}], {x, 0, 37}], x] (* Robert G. Wilson v, Sep 16 2007 *)
CROSSREFS
Column k=2 of A235998.
Cf. A242900 (with distinct multiplicities).
Sequence in context: A015633 A176191 A265248 * A321287 A076664 A220477
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 13 2007
EXTENSIONS
More terms from Robert G. Wilson v, Sep 16 2007
STATUS
approved

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)