A188576 Number of compositions of n with the LMV property.

0, 1, 1, 4, 6, 14, 26, 54, 105, 213, 423, 849, 1697, 3399, 6799, 13608, 27220, 54451, 108901, 217789, 435517, 870892, 1741467, 3482322, 6963512, 13925078, 27846979, 55689150, 111371677, 222735709, 445466058, 890938357, 1781916885, 3563957177, 7128223846

Offset: 1

Author

N. J. A. Sloane, Apr 04 2011

Keywords

• nonn

Comments

A composition has the largest missing value (LMV) property if its largest part is at least 2 and it does not contain a part one less than its largest part. - Andrew Howroyd, May 18 2020

Examples

			The a(5) = 6 compositions of 5 with the LMV property are: 5, 14, 41, 113, 131, 311. - _Andrew Howroyd_, May 18 2020
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000
• M. Archibald and A. Knopfmacher, The largest missing value in a composition of an integer, Discrete Math., 311 (2011), 723-731.

Crossrefs

Cf. A188575, A188577.

Programs

PARI

seq(n)={Vec(sum(k=2, n, 1/(1 - x*(1-x^(k-2))/(1-x) - x^k) - 1/(1 - x*(1-x^(k-2))/(1-x))  + O(x*x^n)), -n)} \\ Andrew Howroyd, May 18 2020

Formula

G.f.: Sum_{k>=2} 1/(1 - x*(1-x^(k-2))/(1-x) - x^k) - 1/(1 - x*(1-x^(k-2))/(1-x)). - Andrew Howroyd, May 18 2020

Extensions

Terms a(21) and beyond from Andrew Howroyd, May 18 2020