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A035622 Number of partitions of n into parts 4k and 4k+2 with at least one part of each type. 3
0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 4, 0, 10, 0, 11, 0, 22, 0, 25, 0, 44, 0, 51, 0, 83, 0, 98, 0, 149, 0, 177, 0, 259, 0, 309, 0, 436, 0, 521, 0, 716, 0, 857, 0, 1151, 0, 1376, 0, 1816, 0, 2170, 0, 2818, 0, 3361, 0, 4309, 0, 5132, 0, 6502, 0, 7728, 0, 9695, 0, 11501, 0, 14298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 101 terms from Robert Price)

FORMULA

G.f.: (-1 + 1/Product_{k>=1} (1 - x^(4 k)))*(-1 + 1/Product_{k>=0} (1 - x^(4 k + 2))). - Robert Price, Aug 16 2020

MATHEMATICA

nmax = 70; s1 = Range[1, nmax/4]*4; s2 = Range[0, nmax/4]*4 + 2;

Table[Count[IntegerPartitions[n, All, s1~Join~s2],

x_ /; ContainsAny[x, s1 ] && ContainsAny[x, s2 ]], {n, 0, nmax}] (* Robert Price, Aug 06 2020 *)

nmax = 70; l = Rest@CoefficientList[Series[(-1 + 1/Product[(1 - x^(4 k)), {k, 1, nmax}])*(-1 + 1/Product[(1 - x^(4 k + 2)), {k, 0, nmax}]), {x, 0, nmax}], x]  (* Robert Price, Aug 16 2020*)

CROSSREFS

Bisections give: A006477 (even part), A000004 (odd part).

Cf. A035441-A035468, A035618-A035621, A035623-A035699.

Sequence in context: A098002 A241658 A256719 * A112919 A019201 A137660

Adjacent sequences:  A035619 A035620 A035621 * A035623 A035624 A035625

KEYWORD

nonn

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 3 14:22 EST 2020. Contains 338906 sequences. (Running on oeis4.)