A133912 -id:A133912 - cp's OEIS frontend

A133913 Array read by ascending antidiagonals generated from partial sums of A007001.

1, 1, 2, 1, 3, 1, 1, 4, 4, 2, 1, 5, 8, 6, 3, 1, 6, 13, 14, 9, 1, 1, 7, 19, 27, 23, 10, 2, 1, 8, 26, 46, 50, 33, 12, 1, 1, 9, 34, 72, 96, 83, 45, 13, 2, 1, 10, 43, 106, 168, 179, 128, 58, 15, 3, 1, 11, 53, 149, 274, 347, 307, 186, 73, 18, 1, 1, 12, 64, 202, 423, 621, 654, 493, 259, 91

Offset: 1

Gary W. Adamson, Sep 28 2007

Given A007001: (1, 2, 1, 2, 3, 1, 2, 1, ...) as first row of an array, n-th row = partial sum sequence of (n-1)-th row.
Row sums = A133914: (1, 3, 5, 11, 23, 44, 89, 177, 355, ...).
Right border = A007001: (1, 2, 1, 2, 3, 1, 2, 1, ...).

			First few rows of the array:
  1, 2,  1,  2,  3,   1,   2, ...
  1, 3,  4,  6,  9,  10,  12, ...
  1, 4,  8, 14, 23,  33,  45, ...
  1, 5, 13, 27, 50,  83, 128, ...
  1, 6, 19, 46, 96, 179, 307, ...
  ...
First few rows of the triangle:
  1;
  1,  2;
  1,  3,  1;
  1,  4,  4,   2;
  1,  5,  8,   6,   3;
  1,  6, 13,  14,   9,   1;
  1,  7, 19,  27,  23,  10,   2;
  1,  8, 26,  46,  50,  33,  12,  1;
  1,  9, 34,  72,  96,  83,  45, 13,  2;
  1, 10, 43, 106, 168, 179, 128, 58, 15, 3;
  ...

Cf. A007001, A133912, A133914.

Edited by Jon E. Schoenfield, Mar 26 2022

A133914 Row sums of triangle A133913.

Original entry on oeis.org

1, 3, 5, 11, 23, 44, 89, 177, 355, 711, 1420, 2841, 5683, 11367, 22731, 45463, 90925, 181851, 363703, 727404, 1454809, 2909617, 5819235, 11638471, 23276940, 46553881, 93107763, 186215527, 372431051, 744862103, 1489724205, 2979448411, 5958896823, 11917793644

Offset: 1

Gary W. Adamson, Sep 28 2007

nonn

			a(4) = 11 = sum of row 4 terms of triangle A133913: (1 + 4 + 4 + 2).
a(4) = 11 = 2*a(3) + A133912(4) = 2*5 + 1, where A133912 = (1, 1, -1, 1, 1, -2, 1, -1, ...), first finite difference row of A007001.

Cf. A007001, A133912, A133913.

a(n) = 2 * a(n-1) + A133912(n). - Jack W Grahl, Oct 11 2022

More terms from Jack W Grahl, Oct 11 2022

cp's OEIS Frontend

A133913 Array read by ascending antidiagonals generated from partial sums of A007001.

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