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 A236758 #30 Nov 06 2024 04:11:17
%S A236758 0,1,3,6,10,14,20,25,32,37,45,51,61,68,79,86,98,106,120,129,144,153,
%T A236758 169,179,196,206,223,233,251,262,282,294,315,327,348,360,382,395,418,
%U A236758 431,455,469,495,510,537,552,580,596,625,641,670,686,716,733,764,781
%N A236758 Number of partitions of 3*n into 3 parts with smallest part prime.
%H A236758 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A236758 a(n) = Sum_{i=1..n} A010051(i) * (2*n - 2*i + 1 - floor((n - i + 1)/2)).
%e A236758 Count the primes in last column for a(n):
%e A236758 13 + 1 + 1
%e A236758 12 + 2 + 1
%e A236758 11 + 3 + 1
%e A236758 10 + 4 + 1
%e A236758 9 + 5 + 1
%e A236758 8 + 6 + 1
%e A236758 7 + 7 + 1
%e A236758 10 + 1 + 1 11 + 2 + 2
%e A236758 9 + 2 + 1 10 + 3 + 2
%e A236758 8 + 3 + 1 9 + 4 + 2
%e A236758 7 + 4 + 1 8 + 5 + 2
%e A236758 6 + 5 + 1 7 + 6 + 2
%e A236758 7 + 1 + 1 8 + 2 + 2 9 + 3 + 3
%e A236758 6 + 2 + 1 7 + 3 + 2 8 + 4 + 3
%e A236758 5 + 3 + 1 6 + 4 + 2 7 + 5 + 3
%e A236758 4 + 4 + 1 5 + 5 + 2 6 + 6 + 3
%e A236758 4 + 1 + 1 5 + 2 + 2 6 + 3 + 3 7 + 4 + 4
%e A236758 3 + 2 + 1 4 + 3 + 2 5 + 4 + 3 6 + 5 + 4
%e A236758 1 + 1 + 1 2 + 2 + 2 3 + 3 + 3 4 + 4 + 4 5 + 5 + 5
%e A236758 3(1) 3(2) 3(3) 3(4) 3(5) .. 3n
%e A236758 ---------------------------------------------------------------------
%e A236758 0 1 3 6 10 .. a(n)
%p A236758 with(numtheory); A236758:=n->sum((pi(n) - pi(n-1)) * (2*n - 2*i + 1 - floor((n - i + 1)/2)), i=1..n); seq(A236758(n), n=1..100);
%t A236758 Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (2 n - 2 i + 1 - Floor[(n - i + 1)/2]), {i, n}], {n, 100}]
%o A236758 (Sage) def a(n): return sum(1 for L in Partitions(3*n,length=3).list() if is_prime(L[2]))
%Y A236758 Cf. A019298, A235988, A236364, A236762, A010051 (for function isprime).
%K A236758 nonn,easy
%O A236758 1,3
%A A236758 _Wesley Ivan Hurt_, Jan 30 2014