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A240139 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 3. 2
1, 0, 1, 0, 2, 0, 3, 0, 4, 1, 5, 2, 7, 4, 8, 7, 10, 12, 12, 18, 14, 27, 17, 38, 21, 53, 26, 71, 33, 94, 44, 121, 58, 155, 79, 194, 107, 241, 146, 296, 197, 361, 267, 436, 355, 525, 472, 628, 618, 750, 805, 894, 1035, 1064, 1324, 1267, 1673, 1511, 2103, 1804 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,5

COMMENTS

With offset 12 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -3.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..1000

FORMULA

a(n) = [x^n y^3] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

EXAMPLE

a(20) = 2: [9,5,3,2,1], [7,5,4,3,1].

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

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, -3):

seq(a(n), n=9..80);

CROSSREFS

Column k=3 of A240021.

Sequence in context: A008735 A239241 A263395 * A008800 A274096 A318518

Adjacent sequences:  A240136 A240137 A240138 * A240140 A240141 A240142

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 02 2014

STATUS

approved

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Last modified November 17 08:39 EST 2019. Contains 329217 sequences. (Running on oeis4.)