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A274174 Number of compositions of n if all summand runs are kept together. 11

%I

%S 1,1,2,4,7,12,22,36,60,97,162,254,406,628,974,1514,2305,3492,5254,

%T 7842,11598,17292,25294,37090,53866,78113,112224,161092,230788,328352,

%U 466040,658846,928132,1302290,1821770,2537156,3536445,4897310,6777806,9341456,12858960,17625970,24133832,32910898,44813228,60922160,82569722

%N Number of compositions of n if all summand runs are kept together.

%C a(n^2) is odd. - _Gregory L. Simay_, Jun 23 2019

%H Alois P. Heinz, <a href="/A274174/b274174.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) = Sum_{k>=0} k! * A116608(n,k). - _Joerg Arndt_, Jun 12 2016

%e 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).

%e 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

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

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

%p end:

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

%p seq(a(n), n=0..50); # _Alois P. Heinz_, Jun 12 2016

%Y Cf. A000070, A116608.

%K nonn

%O 0,3

%A _Gregory L. Simay_, Jun 12 2016

%E Terms a(9) and beyond from _Joerg Arndt_, Jun 12 2016

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Last modified June 1 04:57 EDT 2020. Contains 334758 sequences. (Running on oeis4.)