A070098 Number of integer triangles with perimeter n which are acute and isosceles.

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

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: A341737 A351033 A318837 * A029233 A147981 A051888

Adjacent sequences: A070095 A070096 A070097 * A070099 A070100 A070101

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved