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A070098 Number of integer triangles with perimeter n which are acute and isosceles. 8
0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 4, 4, 5, 4, 5, 5, 6, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 9, 10, 10, 11, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 14, 15, 15, 16, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,9

COMMENTS

Equivalently, the number of obtuse isosceles integer triangles with base n. - Charlie Marion, Jun 18 2019

LINKS

Marius A. Burtea, Table of n, a(n) for n = 1..10000

Reinhard Zumkeller, Integer-sided triangles

FORMULA

a(n) = A070093(n)-A024154(n); a(n) = A059169(n)-A070106(n).

a(n) = floor(n/2) - floor(n/(2 + sqrt(2))) - ((n + 1) mod 2). - David Pasino, Jun 27 2016

a(n) = A004526(n-1) - A183138(n). - R. J. Mathar, May 22 2019

EXAMPLE

For n=9 there are A005044(9)=3 integer triangles: [1,4,4], [2,3,4] and [3,3,3]; both isosceles are also acute.

PROG

(MAGMA) [Floor(k/2)-Floor(k/(2 + Sqrt(2)))-((k + 1) mod 2): k in [1..76]]; // Marius A. Burtea, Jun 21 2019

CROSSREFS

Cf. A070080, A070081, A070082, A059169, A070099, A070100, A070124.

Sequence in context: A010764 A029383 A318837 * A029233 A147981 A051888

Adjacent sequences:  A070095 A070096 A070097 * A070099 A070100 A070101

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, May 05 2002

STATUS

approved

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Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)