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

0,2

Comments

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

Links

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

Formula

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

Example

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;
  ...

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);

Crossrefs

Column k=1 gives A005408.

Row sums give A126646.

Row lengths give A000045(n+1).

Cf. A000244, A337277.

Sequence in context: A316086 A227988 A182813 * A073897 A237058 A285297

Adjacent sequences: A334624 A334625 A334626 * A334628 A334629 A334630

Keyword

nonn,look,tabf

Author

Alois P. Heinz, Sep 09 2020

Status

approved