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 A054582 Array read by antidiagonals upwards: A(m,k) = 2^m * (2k+1), m,k >= 0. 26
 1, 2, 3, 4, 6, 5, 8, 12, 10, 7, 16, 24, 20, 14, 9, 32, 48, 40, 28, 18, 11, 64, 96, 80, 56, 36, 22, 13, 128, 192, 160, 112, 72, 44, 26, 15, 256, 384, 320, 224, 144, 88, 52, 30, 17, 512, 768, 640, 448, 288, 176, 104, 60, 34, 19, 1024, 1536, 1280, 896, 576, 352, 208, 120 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column of array is powers of 2, first row is odd numbers, other cells are products of these two, so every positive integer appears exactly once. [Comment edited to match the definition. - L. Edson Jeffery, Jun 05 2015] An analogous N X N <-> N bijection based, not on the binary, but on the Fibonacci number system, is given by the Wythoff array A035513. As an array, this sequence (hence also A135764) is the dispersion of the even positive integers. For the definition of dispersion, see the link "Interspersions and Dispersions." The fractal sequence of this dispersion is A003602. - Clark Kimberling, Dec 03 2010 LINKS Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened Clark Kimberling, Interspersions and Dispersions. FORMULA As a sequence, if n is a triangular number, then a(n)=a(n-A002024(n))+2, otherwise a(n)=2*a(n-A002024(n)-1). a(n) = A075300(n-1)+1. Recurrence for the sequence: if a(n-1)=2*k is even, then a(n)=k+A006519(2*k); if a(n-1)=2*k+1 is odd, then a(n)=2^(k+1), a(0)=1. - Philippe Deléham, Dec 13 2013 m = A(A001511(m)-1, A003602(m)-1), for each m in A000027. - L. Edson Jeffery, Nov 22 2015 The triangle is T(n, k) = A(n-k, k) = 2^(n-k)*(2*k+1), for n >= 0 and k = 0..n. - Wolfdieter Lang, Jan 30 2019 EXAMPLE Northwest corner of array A:     1     3     5     7     9    11    13    15    17    19     2     6    10    14    18    22    26    30    34    38     4    12    20    28    36    44    52    60    68    76     8    24    40    56    72    88   104   120   136   152    16    48    80   112   144   176   208   240   272   304    32    96   160   224   288   352   416   480   544   608    64   192   320   448   576   704   832   960  1088  1216   128   384   640   896  1152  1408  1664  1920  2176  2432   256   768  1280  1792  2304  2816  3328  3840  4352  4864   512  1536  2560  3584  4608  5632  6656  7680  8704  9728 [Array edited to match the definition. - L. Edson Jeffery, Jun 05 2015] From Philippe Deléham, Dec 13 2013: (Start) a(13-1)=20=2*10, so a(13)=10+A006519(20)=10+4=14. a(3-1)=3=2*1+1, so a(3)=2^(1+1)=4. (End) From Wolfdieter Lang, Jan 30 2019: (Start) The triangle T begins:    n\k   0    1    2   3   4   5   6   7  8  9 10 ...    0:    1    1:    2    3    2:    4    6    5    3:    8   12   10   7    4:   16   24   20  14   9    5:   32   48   40  28  18  11    6:   64   96   80  56  36  22  13    7:  128  192  160 112  72  44  26  15    8:  256  384  320 224 144  88  52  30 17    9:  512  768  640 448 288 176 104  60 34 19   10: 1024 1536 1280 896 576 352 208 120 68 38 21   ... T(3, 2) = 2^1*(2*2+1) = 10. (End) MATHEMATICA (* Array: *) Grid[Table[2^m*(2*k + 1), {m, 0, 9}, {k, 0, 9}]] (* L. Edson Jeffery, Jun 05 2015 *) (* Array antidiagonals flattened: *) Flatten[Table[2^(m - k)*(2*k + 1), {m, 0, 9}, {k, 0, m}]] (* L. Edson Jeffery, Jun 05 2015 *) PROG (Haskell) a054582 n k = a054582_tabl !! n !! k a054582_row n = a054582_tabl !! n a054582_tabl = iterate    (\xs@(x:_) -> (2 * x) : zipWith (+) xs (iterate (`div` 2) (2 * x))) [1] a054582_list = concat a054582_tabl -- Reinhard Zumkeller, Jan 22 2013 (PARI) T(m, k)=(2*k+1)<

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Last modified October 16 08:15 EDT 2019. Contains 328051 sequences. (Running on oeis4.)