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A236758 Number of partitions of 3n into 3 parts with smallest part prime. 5
0, 1, 3, 6, 10, 14, 20, 25, 32, 37, 45, 51, 61, 68, 79, 86, 98, 106, 120, 129, 144, 153, 169, 179, 196, 206, 223, 233, 251, 262, 282, 294, 315, 327, 348, 360, 382, 395, 418, 431, 455, 469, 495, 510, 537, 552, 580, 596, 625, 641, 670, 686, 716, 733, 764, 781 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..56.

Index entries for sequences related to partitions

FORMULA

a(n) = Sum_{i=1..n} A010051(i) * (2n - 2i + 1 - floor((n - i + 1)/2).

EXAMPLE

Count the primes in last column 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           1           3           6           10      ..   a(n)

MAPLE

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);

MATHEMATICA

Table[Sum[(PrimePi[i] - PrimePi[i - 1]) (2 n - 2 i + 1 - Floor[(n - i + 1)/2]), {i, n}], {n, 100}]

PROG

(Sage) def a(n): return sum(1 for L in Partitions(3*n, length=3).list() if is_prime(L[2]))

CROSSREFS

Cf. A019298, A235988, A236364, A236762, A010051 (for function isprime).

Sequence in context: A024928 A330257 A079552 * A272058 A244360 A183863

Adjacent sequences:  A236755 A236756 A236757 * A236759 A236760 A236761

KEYWORD

nonn,easy

AUTHOR

Wesley Ivan Hurt, Jan 30 2014

STATUS

approved

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Last modified February 24 12:13 EST 2020. Contains 332209 sequences. (Running on oeis4.)