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A077229 Number of compositions of n where the largest part is less than or equal to the number of parts. 9
1, 1, 1, 3, 5, 11, 23, 48, 98, 204, 421, 863, 1766, 3606, 7341, 14913, 30233, 61175, 123589, 249344, 502443, 1011366, 2033894, 4086975, 8206833, 16469875, 33035611, 66234372, 132745859, 265961487, 532717894, 1066778687, 2135822457, 4275459730, 8557335141, 17125445575, 34268965676, 68568213419, 137187103849, 274458924246 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
FORMULA
G.f.: 1 + sum(k>=0, ((x^(k+1)-x)/(x-1))^k ). - Vladeta Jovovic, Sep 24 2004
G.f.: 1 + sum(n>=1, q^n * ( (1-q^n)/(1-q) )^n ), the g.f. above, slightly rewritten. [Joerg Arndt, Mar 30 2014]
a(n) ~ 2^(n-1). - Vaclav Kotesovec, May 01 2014
a(n) = A098124(n)+A098125(n). - R. J. Mathar, Oct 01 2021
EXAMPLE
a(5)=11 since 5 can be written as 1+1+1+1+1, 1+1+1+2, 1+1+2+1, 1+1+3, 1+2+1+1, 1+2+2, 1+3+1, 2+1+1+1, 2+1+2, 2+2+1, or 3+1+1; but not as 2+3 since then the largest part (3) would be greater than the number of parts (2).
MATHEMATICA
Table[SeriesCoefficient[1 + Sum[x^k*((1-x^k)/(1-x))^k, {k, 1, n}], {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, May 01 2014 *)
CROSSREFS
Row sums of A077227.
Sequence in context: A030494 A246491 A084361 * A335098 A018113 A113281
KEYWORD
nonn
AUTHOR
Henry Bottomley, Oct 29 2002
EXTENSIONS
More terms from Vladeta Jovovic, Sep 24 2004
Prepended a(0) = 1, Joerg Arndt, Mar 30 2014
STATUS
approved

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Last modified June 13 16:27 EDT 2024. Contains 373389 sequences. (Running on oeis4.)