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A212218 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}. 8
1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 4, 5, 6, 5, 7, 7, 8, 9, 10, 9, 11, 12, 13, 14, 16, 14, 18, 21, 19, 20, 23, 23, 28, 28, 28, 30, 36, 33, 39, 42, 39, 44, 50, 46, 54, 57, 56, 62, 69, 64, 71, 77, 82, 85, 89, 84, 99, 107, 103, 111, 119, 117, 132, 137, 137, 142 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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(4) = 2: 4 = 1*4 = 2*2.

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

a(9) = 3: 9 = 1*1 + 2*4 = 1*9 = 3*3.

a(12) = 4: 12 = 1*2 + 2*5 = 1*12 = 2*6 = 3*4.

a(15) = 5: 15 = 1*3 + 2*6 = 1*3 + 3*4 = 1*1 + 2*7 = 1*15 = 3*5.

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-1), min(j, m/k-1)), 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-1], Min[j, m/k-1]], {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 05 2014, after Alois P. Heinz *)

CROSSREFS

Cf. A066739, A182269, A182270, A211856, A211857, A212214, A212215, A212216, A212217, A212219.

Sequence in context: A194304 A090701 A056970 * A321162 A008668 A225643

Adjacent sequences:  A212215 A212216 A212217 * A212219 A212220 A212221

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 06 2012

STATUS

approved

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Last modified August 24 13:48 EDT 2019. Contains 326279 sequences. (Running on oeis4.)