A140642 -id:A140642 - cp's OEIS frontend

A140643 First differences of A140642.

1, 1, 1, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 8, 8, 2, 1, 1, 4, 16, 16, 4, 1, 1, 2, 8, 32, 32, 8, 2, 1, 1, 4, 16, 64, 64, 16, 4, 1

Offset: 0

Paul Curtz, Jul 08 2008

(*) Main diagonal = A011782 but vertical = 1, A011782 unknown.

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 ] // Differences (* Jean-François Alcover, Dec 16 2014 *)

Also a triangle on line (*): 1; 1, 1; 1, 1, 2; 2, 1, 1, 4; 4, 1, 1, 2, 8; 8, 2, 1, 1, 4, 16; 16, 4, 1, 1, 2, 8, 32; 32, 8, 2, 1, 1, 4, 16, 64; Row sums:1, 2, 4, 8, 16 =A000079(n). Note even palindromes finishing a row and beginning next one.

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

Original entry on oeis.org

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

Paul Curtz, Jul 09 2008

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.

			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;

Cf. A083329 (row sums).

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), ... .

A140951 Based on Jacobsthal numbers. Increasing order of different positive terms of A140950.

Original entry on oeis.org

1, 3, 5, 6, 10, 11, 12, 20, 21, 22, 24, 40, 42, 43, 44, 48, 80, 84, 85, 86, 88, 96, 160, 168, 170, 171, 172, 176, 192, 320, 336, 340, 341, 342, 344, 352, 384, 640

Offset: 0

Paul Curtz, Jul 25 2008

Two possibilities of triangle on line. 1) From 1: 1; 3, 5; 6, 10, 11; 12, 20, 21, 22; 24, 40, 42, 43, 44; . 2) After 1: 3; 5, 6; 10, 11, 12; 20, 21, 22, 24; .

Also A140642 (1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 16, 20) without A000079(n+1). Note position of A001045(n+2) terms: 0, 1, 2, 5, 8, 13 =A000982. See A140503 square .

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A140643 First differences of A140642.

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

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A140951 Based on Jacobsthal numbers. Increasing order of different positive terms of A140950.

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