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A240141 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 5. 2
1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 7, 0, 10, 1, 13, 2, 18, 4, 23, 7, 30, 12, 37, 19, 47, 30, 57, 44, 70, 64, 85, 90, 103, 125, 124, 169, 150, 227, 181, 298, 220, 388, 268, 498, 328, 634, 404, 797, 500, 996, 622, 1232, 775, 1515, 971, 1849, 1216, 2245, 1527, 2708 (list; graph; refs; listen; history; text; internal format)
OFFSET

25,5

COMMENTS

With offset 30 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -5.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 25..1000

FORMULA

a(n) = [x^n y^5] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

EXAMPLE

a(39) = 13: [23,7,5,3,1], [21,9,5,3,1], [19,11,5,3,1], [19,9,7,3,1], [17,13,5,3,1], [17,11,7,3,1], [17,9,7,5,1], [15,13,7,3,1], [15,11,9,3,1], [15,11,7,5,1], [15,9,7,5,3], [13,11,9,5,1], [13,11,7,5,3].

a(40) = 2: [13,9,7,5,3,2,1], [11,9,7,5,4,3,1].

MAPLE

b:= proc(n, i, t) option remember; `if`(n>i*(i+1)/2 or

      abs(t)>n, 0, `if`(n=0, 1, b(n, i-1, t)+

      `if`(i>n, 0, b(n-i, i-1, t+(2*irem(i, 2)-1)))))

    end:

a:= n-> b(n$2, -5):

seq(a(n), n=25..100);

CROSSREFS

Column k=5 of A240021.

Sequence in context: A066682 A239968 A240140 * A049641 A240142 A240143

Adjacent sequences:  A240138 A240139 A240140 * A240142 A240143 A240144

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 02 2014

STATUS

approved

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Last modified June 27 04:02 EDT 2017. Contains 288777 sequences.