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A182831 Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals. 2
1, 2, 3, 4, 6, 8, 5, 11, 17, 22, 7, 14, 28, 45, 55, 9, 19, 37, 70, 112, 137, 10, 23, 48, 93, 171, 276, 334, 12, 26, 57, 118, 228, 417, 671, 812, 13, 31, 66, 141, 287, 556, 1010, 1627, 1965, 15, 34, 77, 164, 344, 697, 1347, 2444, 3934, 4751, 16, 39 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Joint-rank arrays are defined in the first comment at A182801. (row 1)=A087063. First 3 columns are A020062, A020063, A020064.

Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the positive integers.

LINKS

G. C. Greubel, Rows n=1..100 of triangle, flattened

FORMULA

T(i,j) = Sum_{n>=1} floor(j*(1+sqrt(2))^(i-n))).

EXAMPLE

Northwest corner:

   1  2  4  5 ...

   3  6 11 14 ...

   8 17 28 37 ...

  22 45 70 93 ...

  ...

MATHEMATICA

T[n_, k_] := Sum[Floor[k*(1 + Sqrt[2])^(n - j)], {j, 1, 100}]; Table[T[k + 1, n - k], {n, 1, 10}, {k, 0, n-1}]//Flatten (* G. C. Greubel, Aug 18 2018 *)

CROSSREFS

Cf. A182801.

Sequence in context: A257802 A225850 A038150 * A257725 A257690 A336322

Adjacent sequences:  A182828 A182829 A182830 * A182832 A182833 A182834

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Dec 07 2010

STATUS

approved

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Last modified September 24 15:33 EDT 2021. Contains 347643 sequences. (Running on oeis4.)