A182831 Joint-rank array of numbers j*r^(i-1), where r=1+sqrt(2), read by antidiagonals.
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
Offset: 1
Examples
Northwest corner: 1 2 4 5 ... 3 6 11 14 ... 8 17 28 37 ... 22 45 70 93 ... ...
Links
- G. C. Greubel, Rows n=1..100 of triangle, flattened
Crossrefs
Cf. A182801.
Programs
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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 *)
Formula
T(i,j) = Sum_{n>=1} floor(j*(1+sqrt(2))^(i-n)).
Comments