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A212216 Number of representations of n as a sum of products of distinct pairs of positive integers, n = Sum_{k=1..m} i_k*j_k with i_k<=j_k, i_k<=i_{k+1}, j_k<=j_{k+1}, i_k*j_k<i_{k+1}*j_{k+1}. 8
1, 1, 1, 2, 3, 4, 6, 7, 8, 12, 15, 18, 25, 28, 34, 44, 51, 59, 75, 87, 103, 124, 143, 163, 198, 228, 261, 310, 354, 404, 479, 538, 612, 708, 802, 907, 1049, 1175, 1320, 1518, 1711, 1910, 2187, 2431, 2724, 3097, 3447, 3843, 4348, 4818, 5373, 6032, 6693, 7420 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..200

EXAMPLE

a(0) = 1: 0 = the empty sum.

a(1) = 1: 1 = 1*1.

a(2) = 1: 2 = 1*2.

a(3) = 2: 3 = 1*1 + 1*2 = 1*3.

a(4) = 3: 4 = 1*1 + 1*3 = 1*4 = 2*2.

a(5) = 4: 5 = 1*2 + 1*3 = 1*1 + 1*4 = 1*1 + 2*2 = 1*5.

a(6) = 6: 6 = 1*1 + 1*2 + 1*3 = 1*2 + 1*4 = 1*2 + 2*2 = 1*1 + 1+5 = 1*6 = 2*3.

MAPLE

with(numtheory):

b:= proc(n, m, i, j) option remember;

      `if`(n=0, 1, `if`(m<1, 0, b(n, m-1, i, j) +`if`(m>n, 0,

        add(b(n-m, m-1, min(i, k), min(j, m/k)), k=select(x->

         is(x<=min(sqrt(m), i) and m<=j*x), divisors(m))))))

    end:

a:= n-> b(n$4):

seq(a(n), n=0..30);

MATHEMATICA

b[n_, m_, i_, j_] := b[n, m, i, j] = If[n == 0, 1, If[m<1, 0, b[n, m-1, i, j]+If[m>n, 0, Sum [b[n-m, m-1, Min[i, k], Min[j, m/k]], {k, Select[Divisors[m], # <= Min [Sqrt[m], i] && m <= j*# &]}]]]]; a[n_] := b[n, n, n, n]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Dec 04 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A066739, A182269, A182270, A211856, A211857, A212214, A212215, A212217, A212218, A212219.

Sequence in context: A329855 A029748 A018314 * A199639 A215068 A239011

Adjacent sequences:  A212213 A212214 A212215 * A212217 A212218 A212219

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 06 2012

STATUS

approved

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Last modified August 11 09:30 EDT 2020. Contains 336422 sequences. (Running on oeis4.)