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A184639 Number of partitions of n having no parts with multiplicity 4. 8
1, 1, 2, 3, 4, 7, 10, 14, 19, 27, 37, 50, 67, 88, 115, 153, 196, 253, 324, 412, 524, 661, 828, 1036, 1290, 1603, 1980, 2443, 2997, 3671, 4487, 5460, 6631, 8034, 9703, 11703, 14075, 16890, 20226, 24175, 28838, 34332, 40801, 48394, 57307, 67765, 79974 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

a(n) = A000041(n) - A183561(n).

a(n) = A183568(n,0) - A183568(n,4).

G.f.: Product_{j>0} (1-x^(4*j)+x^(5*j))/(1-x^j).

EXAMPLE

a(4) = 4, because 4 partitions of 4 have no parts with multiplicity 4: [1,1,2], [2,2], [1,3], [4].

MAPLE

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

      add((l->`if`(j=4, [l[1]$2], l))(b(n-i*j, i-1)), j=0..n/i)))

    end:

a:= n-> (l-> l[1]-l[2])(b(n, n)):

seq(a(n), n=0..50);

CROSSREFS

Cf. A000041, A183561, A183568, A007690, A116645, A118807, A184640, A184641, A184642, A184643, A184644, A184645.

Sequence in context: A189720 A072958 A062426 * A035565 A240489 A056513

Adjacent sequences:  A184636 A184637 A184638 * A184640 A184641 A184642

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jan 18 2011

STATUS

approved

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Last modified December 2 23:29 EST 2016. Contains 278694 sequences.