The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307728

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A307728

Sum of the perimeters of all acute integer triangles with perimeter n.
(history; published version)

#63 by Wesley Ivan Hurt at Tue Jun 16 14:51:31 EDT 2020

STATUS

editing

approved

#62 by Wesley Ivan Hurt at Tue Jun 16 14:51:25 EDT 2020

LINKS

Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

STATUS

approved

editing

#61 by Wesley Ivan Hurt at Wed May 15 12:15:36 EDT 2019

STATUS

proposed

approved

#60 by Wesley Ivan Hurt at Wed May 15 10:33:27 EDT 2019

STATUS

editing

proposed

#59 by Wesley Ivan Hurt at Wed May 15 09:23:07 EDT 2019

NAME

allocated for Wesley Ivan HurtSum of the perimeters of all acute integer triangles with perimeter n.

DATA

0, 0, 3, 0, 5, 6, 7, 8, 18, 20, 22, 24, 39, 28, 60, 48, 85, 72, 95, 100, 105, 132, 138, 144, 175, 182, 243, 224, 290, 270, 310, 320, 363, 408, 420, 432, 518, 494, 624, 560, 697, 672, 731, 792, 810, 920, 940, 960, 1078, 1100, 1224, 1196, 1325, 1404, 1430

OFFSET

1,3

FORMULA

a(n) = n * A070093(n).

a(n) = n * Sum_{k=1..floor(n/3)} Sum_{i=k..floor((n-k)/2)} (1-sign(floor((n-i-k)^2/(i^2+k^2)))) * sign(floor((i+k)/(n-i-k+1))).

MATHEMATICA

Table[n*Sum[Sum[(1 - Sign[Floor[(n - i - k)^2/(i^2 + k^2)]]) Sign[Floor[(i + k)/(n - i - k + 1)]], {i, k, Floor[(n - k)/2]}], {k, Floor[n/3]}], {n, 100}]

CROSSREFS

Cf. A070093.

KEYWORD

allocated

nonn

AUTHOR

Wesley Ivan Hurt, May 15 2019

STATUS

approved

editing

#58 by Wesley Ivan Hurt at Wed May 15 09:23:07 EDT 2019

NAME

allocated for Wesley Ivan Hurt

KEYWORD

recycled

allocated

#57 by Joerg Arndt at Wed May 15 09:15:53 EDT 2019

STATUS

proposed

approved

#56 by Michel Marcus at Wed May 15 08:51:39 EDT 2019

STATUS

editing

proposed

#55 by Michel Marcus at Wed May 15 08:51:34 EDT 2019

NAME

%k

DATA

1

OFFSET

1

COMMENTS

recycle

EXAMPLE

%k

PROG

%k

CROSSREFS

recycle

KEYWORD

nonn,more,changed

recycled

AUTHOR

recycle

STATUS

proposed

editing

#54 by Daniel Hoyt at Tue May 14 19:52:49 EDT 2019

STATUS

editing

proposed