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A318604 Number of partitions of prime(n) into distinct parts not larger than prime(n-1).

%I A318604 #18 Nov 30 2020 16:19:45
%S A318604 1,1,3,7,16,33,52,99,246,338,750,1255,1608,2585,5110,9782,12074,22240,
%T A318604 32987,40024,70478,101693,173672,345837,483325,570076,789635,927404,
%U A318604 1274113,3725322,5010683,7755766,8953854,18108385,20792118,31316304,46828022,61000699
%N A318604 Number of partitions of prime(n) into distinct parts not larger than prime(n-1).
%C A318604 The first prime number taken into consideration in the sequence is prime(2)=3, as 2 does not have a preceding prime.
%H A318604 Alois P. Heinz, <a href="/A318604/b318604.txt">Table of n, a(n) for n = 2..1000</a>
%e A318604 a(5) = 7: there are 7 partitions of prime(5) = 11 into distinct parts not larger than prime(4) = 7: [7,4], [7,3,1], [6,5], [6,4,1], [6,3,2], [5,4,2], [5,3,2,1].
%p A318604 b:= proc(n,i) option remember; (m-> `if`(m<n, 0, `if`(m=n, 1,
%p A318604       b(n, i-1)+b(n-i, min(n-i, i-1)))))(i*(i+1)/2)
%p A318604     end:
%p A318604 a:= n-> (p-> b(p(n), p(n-1)))(ithprime):
%p A318604 seq(a(n), n=2..50);  # _Alois P. Heinz_, Aug 29 2018
%t A318604 b[n_, i_] := b[n, i] = Function[m, If[m < n, 0, If[m == n, 1, b[n, i - 1] + b[n - i, Min[n - i, i - 1]]]]][i(i+1)/2];
%t A318604 a[n_] := b[Prime[n], Prime[n - 1]];
%t A318604 a /@ Range[2, 50] (* _Jean-François Alcover_, Nov 30 2020, after _Alois P. Heinz_ *)
%K A318604 nonn
%O A318604 2,3
%A A318604 _Pierandrea Formusa_, Aug 29 2018
%E A318604 a(26)-a(39) from _Alois P. Heinz_, Aug 29 2018