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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-François 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 August 1 18:47 EDT 2021. Contains 346402 sequences. (Running on oeis4.)