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A282516 Number T(n,k) of k-element subsets of [n] having a prime element sum; triangle T(n,k), n>=0, 0<=k<=n, read by rows. 13
0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 4, 1, 0, 0, 3, 5, 2, 2, 0, 0, 3, 7, 6, 4, 2, 0, 0, 4, 9, 10, 11, 7, 1, 0, 0, 4, 11, 18, 21, 13, 7, 2, 0, 0, 4, 14, 26, 34, 31, 20, 7, 3, 0, 0, 4, 18, 37, 53, 59, 51, 32, 11, 2, 0, 0, 5, 21, 47, 82, 110, 117, 85, 35, 12, 2, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

LINKS

Alois P. Heinz, Rows n = 0..200, flattened

EXAMPLE

Triangle T(n,k) begins:

  0;

  0, 0;

  0, 1,  1;

  0, 2,  2,  0;

  0, 2,  4,  1,  0;

  0, 3,  5,  2,  2,   0;

  0, 3,  7,  6,  4,   2,   0;

  0, 4,  9, 10, 11,   7,   1,  0;

  0, 4, 11, 18, 21,  13,   7,  2,  0;

  0, 4, 14, 26, 34,  31,  20,  7,  3,  0;

  0, 4, 18, 37, 53,  59,  51, 32, 11,  2, 0;

  0, 5, 21, 47, 82, 110, 117, 85, 35, 12, 2, 0;

MAPLE

b:= proc(n, s) option remember; expand(`if`(n=0,

      `if`(isprime(s), 1, 0), b(n-1, s)+x*b(n-1, s+n)))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=0..n))(b(n, 0)):

seq(T(n), n=0..16);

MATHEMATICA

b[n_, s_] := b[n, s] = Expand[If[n==0, If[PrimeQ[s], 1, 0], b[n-1, s] + x*b[n-1, s+n]]];

T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, n}]][b[n, 0]];

Table[T[n], {n, 0, 16}] // Flatten (* Jean-Fran├žois Alcover, Mar 21 2017, translated from Maple *)

CROSSREFS

Columns k=0-10 give: A000004, A000720, A071917, A320678, A320679, A320680, A320681, A320682, A320683, A320684, A320685.

Row sums give A127542.

Main diagonal gives A185012.

First lower diagonal gives A282518.

T(2n,n) gives A282517.

Sequence in context: A063695 A081417 A133388 * A158092 A145264 A300333

Adjacent sequences:  A282513 A282514 A282515 * A282517 A282518 A282519

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Feb 17 2017

STATUS

approved

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Last modified April 23 06:08 EDT 2019. Contains 322381 sequences. (Running on oeis4.)