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 A236762 Number of partitions of 3n into 3 parts with the middle part prime. 5
 0, 2, 5, 7, 11, 14, 17, 19, 23, 29, 35, 40, 47, 53, 59, 67, 76, 82, 88, 93, 100, 109, 118, 124, 131, 140, 149, 160, 173, 185, 197, 208, 220, 232, 244, 258, 273, 285, 297, 311, 327, 342, 357, 369, 382, 397, 412, 426, 442, 460, 478, 496, 515, 533, 551, 571 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS FORMULA a(n) = Sum_{i=1..n} i * A010051(i) + Sum_{i=1..floor((n - 1)/2)} A010051(n + i) * (n - 2i). EXAMPLE Count the primes in the second columns for a(n):                                                13 + 1 + 1                                                12 + 2 + 1                                                11 + 3 + 1                                                10 + 4 + 1                                                 9 + 5 + 1                                                 8 + 6 + 1                                                 7 + 7 + 1                                    10 + 1 + 1  11 + 2 + 2                                     9 + 2 + 1  10 + 3 + 2                                     8 + 3 + 1   9 + 4 + 2                                     7 + 4 + 1   8 + 5 + 2                                     6 + 5 + 1   7 + 6 + 2                         7 + 1 + 1   8 + 2 + 2   9 + 3 + 3                         6 + 2 + 1   7 + 3 + 2   8 + 4 + 3                         5 + 3 + 1   6 + 4 + 2   7 + 5 + 3                         4 + 4 + 1   5 + 5 + 2   6 + 6 + 3             4 + 1 + 1   5 + 2 + 2   6 + 3 + 3   7 + 4 + 4             3 + 2 + 1   4 + 3 + 2   5 + 4 + 3   6 + 5 + 4 1 + 1 + 1   2 + 2 + 2   3 + 3 + 3   4 + 4 + 4   5 + 5 + 5    3(1)        3(2)        3(3)        3(4)        3(5)     ..   3n --------------------------------------------------------------------     0           2           5           7          11      ..   a(n) MAPLE with(numtheory); A236762:=n->sum( i * (pi(i) - pi(i - 1)), i = 1..n) + sum( (pi(n + i) - pi(n + i - 1)) * (n - 2*i), i = 1..floor((n - 1)/2) ); seq(A236762(n), n=1..100); MATHEMATICA 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}] PROG (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 CROSSREFS Cf. A019298, A235988, A236364, A236758, A010051. Sequence in context: A079379 A287004 A095272 * A327952 A099835 A133436 Adjacent sequences:  A236759 A236760 A236761 * A236763 A236764 A236765 KEYWORD nonn,easy AUTHOR Wesley Ivan Hurt, Jan 30 2014 STATUS approved

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Last modified February 20 07:41 EST 2020. Contains 332069 sequences. (Running on oeis4.)