A291971 -id:A291971 - cp's OEIS frontend

A291970 Triangle read by rows: T(n,k) = 2 * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

1, 0, 2, 0, 2, 0, 2, 4, 0, 2, 4, 0, 2, 8, 0, 2, 8, 8, 0, 2, 12, 8, 0, 2, 12, 16, 0, 2, 16, 24, 0, 2, 16, 32, 16, 0, 2, 20, 40, 16, 0, 2, 20, 56, 32, 0, 2, 24, 64, 48, 0, 2, 24, 80, 80, 0, 2, 28, 96, 96, 32, 0, 2, 28, 112, 144, 32, 0, 2, 32, 128, 176, 64, 0, 2, 32

Offset: 0

Seiichi Manyama, Sep 07 2017

			First few rows are:
  1;
  0, 2;
  0, 2;
  0, 2,  4;
  0, 2,  4;
  0, 2,  8;
  0, 2,  8,  8;
  0, 2, 12,  8;
  0, 2, 12, 16;
  0, 2, 16, 24;
  0, 2, 16, 32, 16.

Seiichi Manyama, Rows n = 0..481, flattened

Row sums give A032302.
Columns 0-1 give A000007, A007395.
Cf. A008289 (m=1), this sequence (m=2), A291971 (m=3).

A292130 Triangle read by rows: T(n,k) = (-3) * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

Original entry on oeis.org

1, 0, -3, 0, -3, 0, -3, 9, 0, -3, 9, 0, -3, 18, 0, -3, 18, -27, 0, -3, 27, -27, 0, -3, 27, -54, 0, -3, 36, -81, 0, -3, 36, -108, 81, 0, -3, 45, -135, 81, 0, -3, 45, -189, 162, 0, -3, 54, -216, 243, 0, -3, 54, -270, 405, 0, -3, 63, -324, 486, -243, 0, -3, 63, -378

Offset: 0

Seiichi Manyama, Sep 09 2017

			First few rows are:
  1;
  0, -3;
  0, -3;
  0, -3,  9;
  0, -3,  9;
  0, -3, 18;
  0, -3, 18,  -27;
  0, -3, 27,  -27;
  0, -3, 27,  -54;
  0, -3, 36,  -81;
  0, -3, 36, -108, 81.

Seiichi Manyama, Rows n = 0..481, flattened

Row sums give A292128.
Columns 0-1 give A000007, (-1)*A010701.
Cf. A291971.

cp's OEIS Frontend

A291970 Triangle read by rows: T(n,k) = 2 * T(n-k,k-1) + T(n-k,k) with T(0,0) = 1 for 0 <= k <= A003056(n).

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