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A171628 Number of compositions of n such that the smallest part is divisible by the number of parts. 1
1, 1, 1, 2, 3, 3, 3, 4, 6, 8, 11, 15, 19, 22, 25, 30, 37, 47, 62, 83, 108, 136, 168, 205, 247, 295, 354, 429, 524, 642, 789, 972, 1196, 1466, 1789, 2173, 2625, 3155, 3778, 4515, 5391, 6437, 7692, 9201, 11014, 13186, 15780, 18865, 22516, 26818, 31871, 37791 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
FORMULA
G.f.: Sum_{n>=0} [Sum_{d|n} x^(n*d)*(1-x^d)/(1-x)^d].
MAPLE
b:= proc(n, t, g) option remember; `if` (n=0, `if` (irem(g, t)=0, 1, 0), add (b(n-i, t+1, min(i, g)), i=1..n)) end: a:= n-> b(n, 0, infinity): seq (a(n), n=1..60); # Alois P. Heinz, Dec 15 2009
A171628 := proc(n) local g, k; g := 0 ; for k from 0 to n do g := g+add (x^(k*d)*(1-x^d)/(1-x)^d, d=numtheory[divisors](k)) ; g := expand(g) ; end do ; coeftayl(g, x=0, n) ; end proc: seq(A171628(n), n=1..60) ; # R. J. Mathar, Dec 14 2009
MATHEMATICA
b[n_, t_, g_] := b[n, t, g] = If[n == 0, If [Mod[g, t] == 0, 1, 0], Sum[b[n - i, t + 1, Min[i, g]], {i, n}]];
a[n_] := b[n, 0, Infinity];
Array[a, 60] (* Jean-François Alcover, May 23 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A327720 A327718 A035581 * A205566 A064338 A197592
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Dec 13 2009
EXTENSIONS
More terms from R. J. Mathar and Alois P. Heinz, Dec 14 2009
STATUS
approved

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Last modified June 22 04:48 EDT 2024. Contains 373565 sequences. (Running on oeis4.)