A136791 Triangle read by rows: (2 * A011971) - A000012.

1, 1, 3, 3, 5, 9, 9, 13, 19, 29, 29, 39, 53, 73, 103, 103, 133, 173, 227, 301, 405, 405, 509, 643, 817, 1045, 1347, 1753, 1753, 2159, 2669, 3313, 4131, 5177, 6525, 8279, 8279, 100033, 12193, 14863, 18177, 22309, 27487, 34013, 42293, 42293, 50573, 60607, 72801, 87665, 105843, 128153, 155641, 189655, 231949

Offset

0,3

Comments

Right border = A060719: (1, 3, 9, 29, 103, ...).

Row sums = A136792.

Links

Table of n, a(n) for n=0..54.

Formula

(2 * A011971) - A000012, where A011971 = Aitken's triangle. Given Aitken's triangle, add 1 immediately after every addition operation. Rightmost term in (n-1)-th row becomes leftmost term in n-th row.

Example

First few rows of the triangle:
    1;
    1,   3;
    3,   5,   9;
    9,  13,  19,  29;
   29,  39,  53,  73, 103;
  103, 133, 173, 227, 301, 405;
  ...

Mathematica

Flatten[Table[2 Sum[Binomial[k, i]*BellB[n - k + i], {i, 0, k}] - 1, {n, 0, 9}, {k, 0, n}]] (* Michael De Vlieger, Apr 02 2022, after Jean-François Alcover at A011971 *)

Crossrefs

Cf. A011971, A136792, A060719.

Sequence in context: A141584 A287195 A179437 * A213933 A091916 A102437

Adjacent sequences: A136788 A136789 A136790 * A136792 A136793 A136794

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 21 2008

Status

approved