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A292961 Rectangular array by antidiagonals:  T(n,m) = rank of n*(r+m) when all the numbers k*(r+h), where r = -1+(1+sqrt(5))/2), k>=1, h>=0, are jointly ranked. 3
1, 3, 2, 6, 8, 4, 9, 15, 13, 5, 12, 22, 25, 19, 7, 17, 30, 38, 35, 27, 10, 20, 40, 52, 54, 48, 33, 11, 24, 49, 66, 74, 72, 61, 41, 14, 28, 58, 82, 93, 98, 91, 73, 46, 16, 32, 67, 96, 115, 124, 122, 108, 85, 55, 18, 37, 78, 111, 136, 151, 155, 146, 129, 101 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

LINKS

Clark Kimberling, Antidiagonals n=1..60, flattened

FORMULA

T(n,m) = Sum_{k=1...[n + m*n/r]} [1 - r + n*(r + m)/k], where r=1/GoldenRatio and [ ]=floor.

EXAMPLE

Northwest corner:

1    3    6    9    12   17   20

2    8    15   22   30   40   49

4    13   25   38   52   66   82

5    19   35   54   74   93   115

7    27   48   72   98   124  151

10   33   61   91   122  155  190

11   41   73   108  146  187  226

14   46   85   129  172  218  266

The numbers k*(r+h), approximately:

(for k=1):   0.618   1.618   2.618 ...

(for k=2):   1.236   3.236   5.236 ...

(for k=3):   1.854   4.854   7.854 ...

Replacing each k*(r+h) by its rank gives

1    3    6

2    8    15

4    13   25

MATHEMATICA

r = -1+GoldenRatio; z = 12;

t[n_, m_] := Sum[Floor[1 - r + n*(r + m)/k], {k, 1, Floor[n + m*n/r]}];

u = Table[t[n, m], {n, 1, z}, {m, 0, z}]; TableForm[u]  (* A292961 array *)

Table[t[n - k + 1, k - 1], {n, 1, z}, {k, n, 1, -1}] // Flatten  (* A292961 sequence *)

CROSSREFS

Cf. A182801, A292959, A292960.

Sequence in context: A209171 A160855 A120232 * A019444 A195412 A069773

Adjacent sequences:  A292958 A292959 A292960 * A292962 A292963 A292964

KEYWORD

nonn,easy,tabl

AUTHOR

Clark Kimberling, Oct 05 2017

STATUS

approved

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Last modified June 4 07:43 EDT 2020. Contains 334822 sequences. (Running on oeis4.)