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A274174 Number of compositions of n if all summand runs are kept together. 11
1, 1, 2, 4, 7, 12, 22, 36, 60, 97, 162, 254, 406, 628, 974, 1514, 2305, 3492, 5254, 7842, 11598, 17292, 25294, 37090, 53866, 78113, 112224, 161092, 230788, 328352, 466040, 658846, 928132, 1302290, 1821770, 2537156, 3536445, 4897310, 6777806, 9341456, 12858960, 17625970, 24133832, 32910898, 44813228, 60922160, 82569722 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n^2) is odd. - Gregory L. Simay, Jun 23 2019

LINKS

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

FORMULA

a(n) = Sum_{k>=0} k! * A116608(n,k). - Joerg Arndt, Jun 12 2016

EXAMPLE

If the summand runs are blocked together, there are 22 compositions of a(6): 6; 5+1, 1+5, 4+2, 2+4, (3+3), 4+(1+1), (1+1)+4, 1+2+3, 1+3+2, 2+1+3, 2+3+1, 3+1+2, 3+2+1, (2+2+2), 3+(1+1+1), (1+1+1)+3, (2+2)+(1+1), (1+1)+(2+2), 2+(1+1+1+1), (1+1+1+1)+2, (1+1+1+1+1+1).

a(0)=1; a(1)= 1; a(4) = 7; a(9) = 97; a(16) = 2305; a(25) = 78113 and a(36) = 3536445. - Gregory L. Simay, Jun 23 19

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0, p!, `if`(i<1, 0,

       add(b(n-i*j, i-1, p+`if`(j=0, 0, 1)), j=0..n/i)))

    end:

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

seq(a(n), n=0..50);  # Alois P. Heinz, Jun 12 2016

CROSSREFS

Cf. A000070, A116608.

Sequence in context: A054151 A018176 A135460 * A089259 A309733 A289107

Adjacent sequences:  A274171 A274172 A274173 * A274175 A274176 A274177

KEYWORD

nonn

AUTHOR

Gregory L. Simay, Jun 12 2016

EXTENSIONS

Terms a(9) and beyond from Joerg Arndt, Jun 12 2016

STATUS

approved

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Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)