The On-Line Encyclopedia of Integer Sequences (OEIS)

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A182846

Joint-rank array of the numbers j*(i-1+r), where r=sqrt(2), i>=1, j>=1, by antidiagonals.
(history; published version)

#8 by Russ Cox at Fri Mar 30 18:57:12 EDT 2012

AUTHOR

_Clark Kimberling (ck6(AT)evansville.edu), _, Dec 08 2010

Discussion

Fri Mar 30

18:57

OEIS Server: https://oeis.org/edit/global/285

#7 by Joerg Arndt at Wed May 18 11:02:42 EDT 2011

STATUS

proposed

approved

#6 by Clark Kimberling at Wed May 18 10:34:56 EDT 2011

FORMULA

T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=sqrt(2), k>=1} for i>=1, j>=1.

MATHEMATICA

r=Sqrt[2];

f[i_, j_]:=Sum[Floor[j*(i-1+r)/(k-1+r)], {k, 1, 1+r+j(i-1+r)}];

TableForm[Table[f[i, j], {i, 1, 10}, {j, 1, 10}]] (*A182846*)

CROSSREFS

Cf. A182801, A182847-A182849.

STATUS

approved

proposed

#5 by T. D. Noe at Wed Dec 08 17:25:31 EST 2010

STATUS

proposed

approved

#4 by Clark Kimberling at Wed Dec 08 16:46:52 EST 2010

FORMULA

T(i,j)=SUM{floor((j*(i-1+r)/(k+r)): r=sqrt(2), k>=1} for i>=1, j>=1.

#3 by Clark Kimberling at Wed Dec 08 16:29:49 EST 2010

NAME

allocated for Clark KimberlingJoint-rank array of the numbers j*(i-1+r), where r=sqrt(2), i>=1, j>=1, by antidiagonals.

DATA

1, 3, 2, 5, 7, 4, 9, 13, 11, 6, 12, 19, 21, 17, 8, 16, 26, 32, 30, 23, 10, 20, 35, 44, 46, 39, 29, 14, 24, 42, 55, 61, 59, 50, 36, 15, 28, 51, 67, 77, 81, 75, 62, 41, 18, 33, 60, 82, 95, 102, 100, 90, 72, 49, 22, 38, 69, 93, 113, 125, 128, 120, 106, 84, 56, 25, 43

OFFSET

1,2

COMMENTS

Joint-rank arrays are defined in the first comment at A182801.

FORMULA

T(i,j)=SUM{floor((j*i-1+r)/(k+r)): r=sqrt(2)} for i>=1, j>=1.

EXAMPLE

Northwest corner:

1....3....5....9...12...

2....7...13...19...26...

4...11...21...32...44...

6...17...30...46...61...

The numbers j*(i-1+sqrt(2)), approximately:

(for i=1) 1.41, 2.83, 4.24,...

(for i=2) 2.41, 4.83, 7.24,...

(for i=3) 3.41, 6.83, 10.24,...

Replacing each by its rank gives

1....3....5

2....7...13

4...ll...21

CROSSREFS

Cf. A182801.

KEYWORD

allocated

nonn,tabl

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu), Dec 08 2010

STATUS

approved

proposed

#2 by Clark Kimberling at Wed Dec 08 16:14:51 EST 2010

KEYWORD

allocating

allocated

#1 by Clark Kimberling at Wed Dec 08 16:14:51 EST 2010

NAME

allocated for Clark Kimberling

KEYWORD

allocating

STATUS

approved