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A102247 Number of partitions of n in which each odd part has odd multiplicity and each even part has even multiplicity. 2
1, 1, 0, 2, 2, 3, 2, 4, 7, 8, 8, 10, 17, 17, 20, 26, 39, 39, 46, 56, 77, 85, 96, 116, 154, 172, 190, 234, 289, 328, 364, 440, 532, 610, 670, 808, 957, 1091, 1204, 1432, 1675, 1905, 2110, 2476, 2867, 3255, 3608, 4184, 4837, 5451, 6050, 6960, 7980, 8961, 9972, 11370 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

G.f.: Product_{i>0} (1+x^(2*i-1)-x^(4*i-2))/(1-x^(2*i)).

a(n) ~ sqrt(Pi^2/3 + 4*log(phi)^2) * exp(sqrt((Pi^2/3 + 4*log(phi)^2)*n)) / (4*Pi*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jan 03 2016

EXAMPLE

a(7) = 4 because we have 7, 322, 22111 and 1111111.

MAPLE

g:=product((1+x^(2*i-1)-x^(4*i-2))/(1-x^(2*i)), i=1..40): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..55); # Emeric Deutsch, Aug 23 2007

# second Maple program:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(`if`(irem(i+j, 2)=0, b(n-i*j, i-1), 0), j=1..n/i)

+b(n, i-1)))

end:

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

seq(a(n), n=0..60); # Alois P. Heinz, May 31 2014

MATHEMATICA

nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k-1) - x^(4*k-2))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 03 2016 *)

CROSSREFS

Cf. A055922, A117958, A130126, A131942, A100847.

Sequence in context: A268327 A053023 A153725 * A054249 A160273 A141822

Adjacent sequences: A102244 A102245 A102246 * A102248 A102249 A102250

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, Aug 16 2007

EXTENSIONS

More terms from Emeric Deutsch, Aug 23 2007

STATUS

approved

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Last modified February 6 17:29 EST 2023. Contains 360110 sequences. (Running on oeis4.)