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A282379 Number of representations of n as a sum of products of pairs of positive integers: n = Sum_{k=1..m} i_k*j_k with m >= 0, i_k <= j_k, j_k > j_{k+1} and all factors distinct with the exception that i_k = j_k is allowed. 2
1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6, 5, 9, 9, 8, 11, 15, 13, 17, 17, 19, 24, 29, 23, 33, 37, 39, 40, 53, 48, 62, 63, 71, 77, 94, 81, 110, 116, 122, 123, 156, 152, 185, 180, 200, 213, 259, 236, 287, 298, 325, 333, 404, 386, 450, 457, 506, 531, 615, 579, 679, 721 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

EXAMPLE

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

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

a(6) = 2: 1*6 = 2*3.

a(7) = 3: 1*7 = 2*3+1*1 = 1*3+2*2.

a(8) = 3: 1*8 = 2*4 = 1*4+2*2.

a(9) = 4: 1*9 = 1*5+2*2 = 2*4+1*1 = 3*3.

a(10) = 5: 1*10 = 1*6+2*2 = 2*5 = 1*4+2*3 = 3*3+1*1.

a(11) = 6: 1*11 = 1*7+2*2 = 2*5+1*1 = 1*5+2*3 = 2*4+1*3 = 3*3+1*2.

a(12) = 5: 1*12 = 1*8+2*2 = 2*6 = 1*6+2*3 = 3*4.

MAPLE

h:= proc(n) option remember;

      n*(n+1)*(2*n+1)/6

    end:

g:= (n, i, s)-> `if`(n=0, 1, `if`(n>h(i), 0,

                b(n, i, select(x-> x<=i, s)))):

b:= proc(n, i, s) option remember; g(n, i-1, s)+

     `if`(i in s, 0, add(`if`(j in s, 0, g(n-i*j,

      min(n-i*j, i-1), s union {j})), j=1..min(i, n/i)))

    end:

a:= n-> g(n$2, {}):

seq(a(n), n=0..100);

CROSSREFS

Cf. A000009, A000330, A066739, A098859, A182269, A182270, A211856, A211857, A212214, A212215, A212216, A212217, A212218, A212219, A276429, A282249.

Sequence in context: A029056 A226503 A036847 * A029055 A035397 A033295

Adjacent sequences:  A282376 A282377 A282378 * A282380 A282381 A282382

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 13 2017

STATUS

approved

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Last modified May 17 00:16 EDT 2021. Contains 343957 sequences. (Running on oeis4.)