This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A236762 #28 Jul 30 2019 17:44:32
%S A236762 0,2,5,7,11,14,17,19,23,29,35,40,47,53,59,67,76,82,88,93,100,109,118,
%T A236762 124,131,140,149,160,173,185,197,208,220,232,244,258,273,285,297,311,
%U A236762 327,342,357,369,382,397,412,426,442,460,478,496,515,533,551,571
%N A236762 Number of partitions of 3n into 3 parts with the middle part prime.
%H A236762 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A236762 a(n) = Sum_{i=1..n} i * A010051(i) + Sum_{i=1..floor((n - 1)/2)} A010051(n + i) * (n - 2i).
%e A236762 Count the primes in the second columns for a(n):
%e A236762 13 + 1 + 1
%e A236762 12 + 2 + 1
%e A236762 11 + 3 + 1
%e A236762 10 + 4 + 1
%e A236762 9 + 5 + 1
%e A236762 8 + 6 + 1
%e A236762 7 + 7 + 1
%e A236762 10 + 1 + 1 11 + 2 + 2
%e A236762 9 + 2 + 1 10 + 3 + 2
%e A236762 8 + 3 + 1 9 + 4 + 2
%e A236762 7 + 4 + 1 8 + 5 + 2
%e A236762 6 + 5 + 1 7 + 6 + 2
%e A236762 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
%e A236762 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
%e A236762 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
%e A236762 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
%e A236762 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
%e A236762 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
%e A236762 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
%e A236762 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
%e A236762 --------------------------------------------------------------------
%e A236762 0 2 5 7 11 .. a(n)
%p A236762 with(numtheory); A236762:=n->sum( i * (pi(i) - pi(i - 1)), i = 1..n) +
%p A236762 sum( (pi(n + i) - pi(n + i - 1)) * (n - 2*i), i = 1..floor((n - 1)/2) ); seq(A236762(n), n=1..100);
%t A236762 Table[Sum[i (PrimePi[i] - PrimePi[i - 1]), {i, n}] + Sum[(PrimePi[n + i] - PrimePi[n + i - 1]) (n - 2 i), {i, Floor[(n - 1)/2]}], {n, 100}]
%o A236762 (Sage) def a(n): return sum(1 for L in Partitions(3*n,length=3).list() if is_prime(L[1])) # _Ralf Stephan_, Feb 03 2014
%Y A236762 Cf. A019298, A235988, A236364, A236758, A010051.
%K A236762 nonn,easy
%O A236762 1,2
%A A236762 _Wesley Ivan Hurt_, Jan 30 2014