A077229 Number of compositions of n where the largest part is less than or equal to the number of parts.

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

Offset

0,4

Links

Table of n, a(n) for n=0..39.

Index entries for sequences related to compositions

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.

Cf. A064174, A348125.

Sequence in context: A030494 A246491 A084361 * A335098 A018113 A113281

Adjacent sequences: A077226 A077227 A077228 * A077230 A077231 A077232

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