A140642 Triangle of sorted absolute values of Jacobsthal successive differences.

1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 16, 20, 21, 22, 24, 32, 40, 42, 43, 44, 48, 64, 80, 84, 85, 86, 88, 96, 128, 160, 168, 170, 171, 172, 176, 192, 256, 320, 336, 340, 341, 342, 344, 352, 384, 512, 640, 672, 680, 682, 683, 684, 688, 704, 768, 1024, 1280, 1344, 1360

Offset: 0

Author

Paul Curtz, Jul 08 2008

Keywords

• nonn
• tabl

Comments

The triangle is generated from the set of Jacobsthal numbers A001045 and all the iterated differences (see A078008, A084247), taking the absolute values and sorting into natural order.

The first differences generated individually along any row of this triangle here are all in A000079.

Examples

			The triangle starts
   1;
   2,  3;
   4,  5,  6;
   8, 10, 11, 12;
  16, 20, 21, 22, 24;
The Jacobsthal sequence and its differences in successive rows start:
    0,   1,   1,   3,   5,  11,  21,  43,  85, ...
    1,   0,   2,   2,   6,  10,  22,  42,  86, ...
   -1,   2,   0,   4,   4,  12,  20,  44,  84, ...
    3,  -2,   4,   0,   8,   8,  24,  40,  88, ...
   -5,   6,  -4,   8,   0,  16,  16,  48,  80, ...
   11, -10,  12,  -8,  16,   0,  32,  32,  96, ...
  -21,  22, -20,  24, -16,  32,   0,  64,  64, ...
   43, -42,  44, -40,  48, -32,  64,   0, 128, ...
The values +-7, +-9, +-13, for example, are missing there, so 7, 9 and 13 are not in the triangle.
		

Crossrefs

Cf. A000079, A003945, A078008, A084247, A113861.

Programs

Mathematica

maxTerm = 384; FixedPoint[(nMax++; Print["nMax = ", nMax]; jj = Table[(2^n - (-1)^n)/3, {n, 0, nMax}]; Table[Differences[jj, n], {n, 0, nMax}] // Flatten // Abs // Union // Select[#, 0 < # <= maxTerm &] &) &, nMax = 5 ] (* Jean-François Alcover, Dec 16 2014 *)

Formula

Row sums: A113861(n+2).

Extensions

Edited by R. J. Mathar, Dec 05 2008

a(45)-a(58) from Stefano Spezia, Mar 12 2024