A140648 Triangle T(n,m) which can create A140642 without help of Jacobsthal numbers.

1, 2, 0, 4, 1, 0, 8, 2, 0, 1, 16, 4, 1, 0, 2, 32, 8, 2, 0, 1, 4, 64, 16, 4, 1, 0, 2, 8, 128, 32, 8, 2, 0, 1, 4, 16, 256, 64, 16, 4, 1, 0, 2, 8, 32, 512, 128, 32, 8, 2, 0, 1, 4, 16, 64

Offset

0,2

Comments

This triangle T(.,.) provides the additional terms if A140642 is constructed with a Pascal-type recurrence: A140642(n+1,m+1) = A140642(n,m) + A140642(n,m+1) + T(n,m+1).

Note almost odd palindromes (of squares) followed by their double.

Examples: 40=16+20+4, 42=20+21+1, 43=21+22+0, 44=22+24+2.

Links

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

Formula

Southeast diagonals based on A131577 (which is also in A140531). First preceded with 1, 0. Second with 2, 1, 0. Tends towards even palindromes, second part being A131577. Verticals: A000079, A131577, (0, A131577), ... .

Example

Triangle begins:
    1;
    2,  0;
    4,  1,  0;
    8,  2,  0,  1;
   16,  4,  1,  0,  2;
   32,  8,  2,  0,  1,  4;
   64, 16,  4,  1,  0,  2,  8;
  128, 32,  8,  2,  0,  1,  4, 16;

Crossrefs

Cf. A083329 (row sums).

Sequence in context: A255330 A291940 A153345 * A153342 A144258 A056859

Adjacent sequences: A140645 A140646 A140647 * A140649 A140650 A140651

Keyword

nonn,tabl,uned

Author

Paul Curtz, Jul 09 2008

Status

approved