The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A182849 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A182849

Joint-rank array of the numbers j*(i-1+r), where r = golden ratio = (1+sqrt(5))/2, and i>=1, j>=1, by antidiagonals.
(history; published version)

#6 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

#5 by Joerg Arndt at Thu May 19 02:25:44 EDT 2011

STATUS

proposed

approved

#4 by Clark Kimberling at Wed May 18 10:41:40 EDT 2011

FORMULA

T(i,j)=SUM{floor(j*(i-1+r)/(k-1+r)): r=(1+sqrt(5))/2, k>=1} for i>=1, j>=1.

MATHEMATICA

r=GoldenRatio;

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}]] (* A182849 *)

STATUS

approved

proposed

#3 by T. D. Noe at Wed Dec 08 17:26:04 EST 2010

STATUS

proposed

approved

#2 by Clark Kimberling at Wed Dec 08 17:04:53 EST 2010

NAME

allocated for Clark KimberlingJoint-rank array of the numbers j*(i-1+r), where r = golden ratio = (1+sqrt(5))/2, and i>=1, j>=1, by antidiagonals.

DATA

1, 3, 2, 6, 7, 4, 9, 13, 11, 5, 14, 19, 21, 16, 8, 18, 27, 31, 30, 22, 10, 23, 36, 43, 45, 39, 28, 12, 26, 44, 56, 61, 57, 50, 34, 15, 32, 52, 68, 78, 79, 73, 60, 40, 17, 37, 63, 83, 94, 101, 98, 87, 70, 47, 20, 42, 72, 96, 113, 124, 126, 118, 104, 82, 54, 24, 48

OFFSET

1,2

COMMENTS

Joint-rank arrays are defined in the first comment at A182801. Every positive integer occurs exactly once, so that as a sequence, A182849 is a permutation of the positive integers.

FORMULA

T(i,j)=SUM{floor(j*(i-1+r)/(k+r)): r=(1+sqrt(5))/2, k>=1} for i>=1, j>=1.

EXAMPLE

Northwest corner:

1....3....6....9...

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

4...11...21...31...

5...16...30...45...

CROSSREFS

Cf. A182801, A182846.

KEYWORD

allocated

nonn,tabl

AUTHOR

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

STATUS

approved

proposed

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

NAME

allocated for Clark Kimberling

KEYWORD

allocated

STATUS

approved