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 A181851 Triangle read by rows: T(n,k) = Sum_{c in composition(n,k)} lcm(c). 3

%I #16 Mar 13 2018 04:06:45

%S 1,2,1,3,4,1,4,8,6,1,5,20,15,8,1,6,21,50,24,10,1,7,56,66,96,35,12,1,8,

%T 60,180,160,160,48,14,1,9,96,264,432,325,244,63,16,1,10,105,510,776,

%U 892,585,350,80,18,1,11,220,567,1704,1835,1668,966,480,99,20,1

%N Triangle read by rows: T(n,k) = Sum_{c in composition(n,k)} lcm(c).

%C Composition(n,k) is the set of the k-tuples of positive integers which sum to n (see A181842). Taking the example in A181842, T(6,2) = lcm(5,1) + lcm(4,2) + lcm(3,3) + lcm(2,4) + lcm(1,5) = 5+4+3+4+5 = 21.

%H Alois P. Heinz, <a href="/A181851/b181851.txt">Rows n = 1..25, flattened</a>

%e [1] 1

%e [2] 2 1

%e [3] 3 4 1

%e [4] 4 8 6 1

%e [5] 5 20 15 8 1

%e [6] 6 21 50 24 10 1

%e [7] 7 56 66 96 35 12 1

%p with(combstruct):

%p a181851_row := proc(n) local k,L,l,R,comp;

%p R := NULL;

%p for k from 1 to n do

%p L := 0;

%p comp := iterstructs(Composition(n),size=k):

%p while not finished(comp) do

%p l := nextstruct(comp);

%p L := L + ilcm(op(l));

%p od;

%p R := R,L;

%p od;

%p R end:

%t c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[t[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 05 2014 *)

%Y Cf. A181849, A181850, A181853.

%K nonn,tabl

%O 1,2

%A _Peter Luschny_, Dec 07 2010

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Last modified April 14 17:14 EDT 2024. Contains 371666 sequences. (Running on oeis4.)