A334627 T(n,k) is the number of k's in the n-th row of Stern's triangle (A337277); triangle T(n,k), n >= 0, 1 <= k <= A000045(n+1), read by rows.

1, 3, 5, 2, 7, 4, 4, 9, 6, 8, 4, 4, 11, 8, 12, 8, 12, 0, 8, 4, 13, 10, 16, 12, 20, 4, 16, 8, 8, 4, 8, 4, 4, 15, 12, 20, 16, 28, 8, 28, 12, 16, 8, 24, 8, 16, 8, 4, 4, 8, 8, 8, 0, 4, 17, 14, 24, 20, 36, 12, 40, 20, 24, 12, 40, 12, 36, 16, 8, 16, 28, 16, 24, 4, 8, 8, 16, 4, 12, 8, 8, 0, 12, 4, 8, 0, 0, 4

Offset: 0

Author

Alois P. Heinz, Sep 09 2020

Keywords

• nonn
• look
• tabf

Comments

All terms in the first column are odd, all other terms are even.

Examples

			T(0,1) = 1 because Stern's triangle has one 1 in row n=0.
T(2,2) = 2 because Stern's triangle has two 2's in row n=2.
T(4,3) = 8 because Stern's triangle has eight 3's in row n=4.
Triangle T(n,k) begins:
   1;
   3;
   5,  2;
   7,  4,  4;
   9,  6,  8,  4,  4;
  11,  8, 12,  8, 12, 0,  8,  4;
  13, 10, 16, 12, 20, 4, 16,  8,  8, 4,  8, 4,  4;
  15, 12, 20, 16, 28, 8, 28, 12, 16, 8, 24, 8, 16, 8, 4, 4, 8, 8, 8, 0, 4;
  ...
		

Links

• Alois P. Heinz, Rows n = 0..21, flattened

Crossrefs

Column k=1 gives A005408.

Row sums give A126646.

Row lengths give A000045(n+1).

Cf. A000244, A337277.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, [1], (l-> [1, l[1],
      seq([l[i-1]+l[i], l[i]][], i=2..nops(l)), 1])(b(n-1)))
    end:
T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(add(x^j, j=b(n))):
seq(T(n), n=0..8);

Formula

Sum_{k=1..A000045(n+1)} k * T(n,k) = A000244(n).