A181851 -id:A181851 - cp's OEIS frontend

A181849 Row sums of A181851.

1, 1, 3, 8, 19, 49, 112, 273, 631, 1450, 3327, 7571, 17170, 38519, 85951, 190392, 419759, 921189, 2013874, 4385889, 9516273, 20577618, 44352499, 95324853, 204307052, 436768151, 931448065, 1981879262, 4207887155, 8916102661, 18856430826, 39807226901, 83892649091

Offset: 0

Peter Luschny, Dec 07 2010

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..150

Cf. A181850, A181851.

with(combstruct):
a181849 := proc(n) local k,L,l,comp;
L := 1-signum(n);
for k from 1 to n do
   comp := iterstructs(Composition(n),size=k):
   while not finished(comp) do
      l := nextstruct(comp);
      L := L + ilcm(op(l));
   od;
od;
L end:
seq(a181849(n), n=0..15);

c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[Print[s = Sum[t[n, k], {k, 1, n}]]; s, {n, 1, 25}]  (* Jean-François Alcover, Feb 05 2014 *)

a(23)-a(25) from Alois P. Heinz, Jul 29 2013

a(0), a(26)-a(32) from Alois P. Heinz, Jun 18 2024

A181850 Triangle read by rows: Partial row sums of A181851(n,k).

Original entry on oeis.org

1, 2, 3, 3, 7, 8, 4, 12, 18, 19, 5, 25, 40, 48, 49, 6, 27, 77, 101, 111, 112, 7, 63, 129, 225, 260, 272, 273, 8, 68, 248, 408, 568, 616, 630, 631, 9, 105, 369, 801, 1126, 1370, 1433, 1449, 1450, 10, 115, 625, 1401, 2293, 2878, 3228, 3308, 3326, 3327

Offset: 1

Peter Luschny, Dec 07 2010

			[1]   1
[2]   2    3
[3]   3    7     8
[4]   4   12    18    19
[5]   5   25    40    48    49
[6]   6   27    77   101   111   112
[7]   7   63   129   225   260   272   273

Alois P. Heinz, Rows n = 1..25, flattened

Cf. A181849, A181851, A181854.

with(combstruct):
a181850_row := proc(n) local k,L,l,R,comp;
R := NULL; L := 0;
for k from 1 to n do
   comp := iterstructs(Composition(n),size=k):
   while not finished(comp) do
      l := nextstruct(comp);
      L := L + ilcm(op(l));
   od;
   R := R,L;
od;
R end:

c[n_, k_] := Permutations /@ IntegerPartitions[n, {k}] // Flatten[#, 1]&; t[n_, k_] := Total[LCM @@@ c[n, k]]; Table[Print[row = Table[t[n, k], {k, 1, n}] // Accumulate]; row, {n, 1, 25}] // Flatten  (* Jean-François Alcover, Feb 05 2014 *)

A373865 Sum over all compositions of 2n into n parts of the least common multiple of the parts.

Original entry on oeis.org

1, 2, 8, 50, 160, 892, 3794, 19560, 80112, 371948, 1614598, 7180494, 30794746, 134269410, 574754496, 2471353090, 10542096528, 45057428356, 191653403306, 814082549052, 3444043955350, 14537736838038, 61174002263338, 256838845740468, 1075631257186986

Offset: 0

Alois P. Heinz, Jun 19 2024

nonn

			a(3) = 50 = 2 + 6*6 + 3*4: 222, 123, 132, 213, 231, 312, 321, 114, 141, 411.

Alois P. Heinz, Table of n, a(n) for n = 0..75

Cf. A005430 (the same for sum), A165817 (the same for product), A181851, A260878 (the same for gcd).

a(n) = A181851(2n,n).

cp's OEIS Frontend

A181849 Row sums of A181851.

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A181850 Triangle read by rows: Partial row sums of A181851(n,k).

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Maple

Mathematica

A373865 Sum over all compositions of 2n into n parts of the least common multiple of the parts.

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