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A240140 Number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is 4. 2
1, 0, 1, 0, 2, 0, 3, 0, 5, 0, 6, 1, 9, 2, 11, 4, 15, 7, 18, 12, 23, 19, 27, 29, 34, 42, 40, 60, 49, 83, 59, 113, 73, 150, 89, 197, 112, 254, 141, 324, 180, 408, 231, 509, 298, 629, 386, 771, 500, 938, 648, 1135, 835, 1365, 1076, 1634, 1376, 1949, 1755, 2317 (list; graph; refs; listen; history; text; internal format)
OFFSET

16,5

COMMENTS

With offset 20 number of partitions of n into distinct parts, where the difference between the number of odd parts and the number of even parts is -4.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 16..1000

FORMULA

a(n) = [x^n y^4] Product_{i>=1} 1+x^i*y^(2*(i mod 2)-1).

EXAMPLE

a(28) = 9: [19,5,3,1], [17,7,3,1], [15,9,3,1], [15,7,5,1], [13,11,3,1], [13,9,5,1], [13,7,5,3], [11,9,7,1], [11,9,5,3].

a(29) = 2: [11,7,5,3,2,1], [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, -4):

seq(a(n), n=16..80);

CROSSREFS

Column k=4 of A240021.

Sequence in context: A066682 A239968 A320311 * A240141 A049641 A240142

Adjacent sequences:  A240137 A240138 A240139 * A240141 A240142 A240143

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Apr 02 2014

STATUS

approved

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)