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A140642 Triangle of sorted absolute values of Jacobsthal successive differences.

%I A140642 #25 Apr 24 2024 09:18:09
%S A140642 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,
%T A140642 86,88,96,128,160,168,170,171,172,176,192,256,320,336,340,341,342,344,
%U A140642 352,384,512,640,672,680,682,683,684,688,704,768,1024,1280,1344,1360
%N A140642 Triangle of sorted absolute values of Jacobsthal successive differences.
%C A140642 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.
%C A140642 The first differences generated individually along any row of this triangle here are all in A000079.
%F A140642 Row sums: A113861(n+2).
%e A140642 The triangle starts
%e A140642    1;
%e A140642    2,  3;
%e A140642    4,  5,  6;
%e A140642    8, 10, 11, 12;
%e A140642   16, 20, 21, 22, 24;
%e A140642 The Jacobsthal sequence and its differences in successive rows start:
%e A140642     0,   1,   1,   3,   5,  11,  21,  43,  85, ...
%e A140642     1,   0,   2,   2,   6,  10,  22,  42,  86, ...
%e A140642    -1,   2,   0,   4,   4,  12,  20,  44,  84, ...
%e A140642     3,  -2,   4,   0,   8,   8,  24,  40,  88, ...
%e A140642    -5,   6,  -4,   8,   0,  16,  16,  48,  80, ...
%e A140642    11, -10,  12,  -8,  16,   0,  32,  32,  96, ...
%e A140642   -21,  22, -20,  24, -16,  32,   0,  64,  64, ...
%e A140642    43, -42,  44, -40,  48, -32,  64,   0, 128, ...
%e A140642 The values +-7, +-9, +-13, for example, are missing there, so 7, 9 and 13 are not in the triangle.
%t A140642 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 *)
%Y A140642 Cf. A000079, A003945, A078008, A084247, A113861.
%K A140642 nonn,tabl
%O A140642 0,2
%A A140642 _Paul Curtz_, Jul 08 2008
%E A140642 Edited by _R. J. Mathar_, Dec 05 2008
%E A140642 a(45)-a(58) from _Stefano Spezia_, Mar 12 2024