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

1,4

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

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.

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

Example

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

Prog

(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

Crossrefs

Cf. A188575, A188577.

Sequence in context: A370410 A192782 A306742 * A084214 A030138 A369684

Adjacent sequences: A188573 A188574 A188575 * A188577 A188578 A188579

Keyword

nonn

Author

N. J. A. Sloane, Apr 04 2011

Extensions

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

Status

approved