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A212548 Number of partitions of n containing at least one part m-8 if m is the largest part. 2
0, 0, 1, 1, 3, 4, 8, 11, 19, 26, 41, 56, 82, 110, 156, 205, 281, 366, 488, 627, 821, 1041, 1340, 1684, 2135, 2657, 3331, 4108, 5095, 6238, 7663, 9315, 11354, 13709, 16588, 19915, 23936, 28580, 34154, 40573, 48225, 57031, 67452, 79428, 93530, 109695, 128639 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..1000

FORMULA

G.f.: Sum_{i>0} x^(2*i+8) / Product_{j=1..8+i} (1-x^j).

EXAMPLE

a(10) = 1: [9,1].

a(11) = 1: [9,1,1].

a(12) = 3: [9,1,1,1], [9,2,1], [10,2].

a(13) = 4: [9,1,1,1,1], [9,2,1,1], [9,3,1], [10,2,1].

a(14) = 8: [9,1,1,1,1,1], [9,2,1,1,1], [9,2,2,1], [9,3,1,1], [9,4,1], [10,2,1,1], [10,2,2], [11,3].

MAPLE

b:= proc(n, i) option remember;

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

    end:

a:= n-> add(b(n-2*m-8, min(n-2*m-8, m+8)), m=1..(n-8)/2):

seq(a(n), n=8..60);

MATHEMATICA

Table[Count[IntegerPartitions[n], _?(MemberQ[#, Max[#]-8]&)], {n, 8, 55}] (* Harvey P. Dale, May 05 2016 *)

CROSSREFS

Column k=8 of A212551.

Sequence in context: A212545 A212546 A212547 * A212549 A212550 A024786

Adjacent sequences:  A212545 A212546 A212547 * A212549 A212550 A212551

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 20 2012

STATUS

approved

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Last modified April 22 14:33 EDT 2019. Contains 322356 sequences. (Running on oeis4.)