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A118096 Number of partitions of n such that the largest part is twice the smallest part. 9
0, 0, 1, 1, 2, 3, 3, 4, 6, 6, 6, 10, 9, 11, 13, 14, 15, 20, 18, 23, 25, 27, 27, 37, 35, 39, 43, 48, 49, 61, 57, 68, 72, 78, 81, 97, 95, 107, 114, 127, 128, 150, 148, 168, 179, 191, 198, 229, 230, 254, 266, 291, 300, 338, 344, 379, 398, 427, 444, 498, 505, 550, 580, 625 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Also number of partitions of n such that if the largest part occurs k times, then the number of parts is 2k. Example: a(8)=4 because we have [7,1], [6,2], [5,3] and [3,3,1,1].

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

G.f.: sum(k>=1, x^(3*k)/prod(j=k..2*k, 1-x^j ) ).

EXAMPLE

a(8)=4 because we have [4,2,2], [2,2,2,1,1], [2,2,1,1,1,1] and [2,1,1,1,1,1,1].

MAPLE

g:=sum(x^(3*k)/product(1-x^j, j=k..2*k), k=1..30): gser:=series(g, x=0, 75): seq(coeff(gser, x, n), n=1..70);

# second Maple program:

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

       b(n, i-1, t)+`if`(i>n, 0, b(n-i, i, t))))

    end:

a:= n-> add(b(n-3*j, 2*j, j), j=1..n/3):

seq(a(n), n=1..64);  # Alois P. Heinz, Sep 04 2017

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; 2 Min[p] = = Max[p]], {n, 40}] (* Clark Kimberling, Feb 16 2014 *)

CROSSREFS

Sequence in context: A290585 A106464 A093003 * A296440 A181692 A145806

Adjacent sequences:  A118093 A118094 A118095 * A118097 A118098 A118099

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Apr 12 2006

STATUS

approved

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)