cp's OEIS Frontend

A212547 Number of partitions of n containing at least one part m-7 if m is the largest part.

%I A212547 #13 Dec 07 2020 08:11:00
%S A212547 0,0,1,1,3,4,8,11,19,26,41,55,81,108,152,199,272,351,467,596,776,979,
%T A212547 1255,1566,1978,2448,3054,3747,4628,5635,6896,8342,10125,12172,14673,
%U A212547 17537,21005,24981,29748,35210,41718,49161,57974,68049,79902,93440,109295
%N A212547 Number of partitions of n containing at least one part m-7 if m is the largest part.
%H A212547 Alois P. Heinz, <a href="/A212547/b212547.txt">Table of n, a(n) for n = 7..1000</a>
%F A212547 G.f.: Sum_{i>0} x^(2*i+7) / Product_{j=1..7+i} (1-x^j).
%e A212547 a(9) = 1: [8,1].
%e A212547 a(10) = 1: [8,1,1].
%e A212547 a(11) = 3: [8,1,1,1], [8,2,1], [9,2].
%e A212547 a(12) = 4: [8,1,1,1,1], [8,2,1,1], [8,3,1], [9,2,1].
%e A212547 a(13) = 8: [8,1,1,1,1,1], [8,2,1,1,1], [8,2,2,1], [8,3,1,1], [8,4,1], [9,2,1,1], [9,2,2], [10,3].
%p A212547 b:= proc(n, i) option remember;
%p A212547       `if`(n=0 or i=1, 1, b(n, i-1)+`if`(i>n, 0, b(n-i, i)))
%p A212547     end:
%p A212547 a:= n-> add(b(n-2*m-7, min(n-2*m-7, m+7)), m=1..(n-7)/2):
%p A212547 seq(a(n), n=7..60);
%t A212547 b[n_, i_] := b[n, i] = If[n == 0 || i == 1, 1, b[n, i - 1] + If[i > n, 0, b[n - i, i]]];
%t A212547 a[n_] := Sum[b[n - 2 m - 7, Min[n - 2 m - 7, m + 7]], {m, 1, (n - 7)/2}];
%t A212547 a /@ Range[7, 60] (* _Jean-François Alcover_, Dec 07 2020, after _Alois P. Heinz_ *)
%Y A212547 Column k=7 of A212551.
%K A212547 nonn
%O A212547 7,5
%A A212547 _Alois P. Heinz_, May 20 2012