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A336718 Total number of left-to-right maxima in all compositions of n into distinct parts. 4
0, 1, 1, 4, 4, 7, 18, 21, 32, 46, 107, 121, 193, 257, 379, 728, 900, 1299, 1806, 2529, 3360, 6182, 7387, 10807, 14385, 20217, 26207, 36450, 58194, 72887, 101130, 135379, 183178, 240796, 323307, 417625, 649959, 797623, 1096645, 1426108, 1931340, 2470541 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Also total number of left-to-right minima in all compositions of n into distinct parts.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

FORMULA

a(n) = Sum_{k=1..floor((sqrt(8*n+1)-1)/2)} A000254(k) * A008289(n,k).

EXAMPLE

a(6) = 18 = 3+2+2+2+1+1+2+1+2+1+1: (1)(2)(3), (1)(3)2, (2)1(3), (2)(3)1, (3)12, (3)21, (2)(4), (4)2, (1)(5), (5)1, (6).

MAPLE

g:= proc(n) option remember;

      `if`(n<2, n, (2*n-1)*g(n-1)-(n-1)^2*g(n-2))

    end:

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,

      `if`(n=0, g(p), b(n, i-1, p)+b(n-i, min(n-i, i-1), p+1)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..50);

CROSSREFS

Cf. A000254, A003056, A008289, A032020, A336482, A336770, A336771.

Sequence in context: A115292 A202676 A330765 * A173324 A318243 A321661

Adjacent sequences:  A336715 A336716 A336717 * A336719 A336720 A336721

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Aug 01 2020

STATUS

approved

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Last modified September 20 07:21 EDT 2020. Contains 337264 sequences. (Running on oeis4.)