

A236384


Number of noncongruent integer triangles with base length n whose apex lies on or within a space bounded by a semicircle of diameter n.


3



0, 0, 1, 1, 3, 4, 5, 7, 10, 13, 15, 17, 22, 25, 30, 33, 38, 42, 48, 54, 58, 65, 71, 76, 85, 92, 100, 106, 114, 123, 130, 140, 149, 159, 170, 177, 189, 197, 211, 222, 231, 243, 255, 269, 282, 292, 306, 318, 333, 348, 364, 378, 391, 406, 420, 438, 453, 470, 485
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OFFSET

1,5


COMMENTS

Number of integer sided obtuse or right (nonacute) triangles with largest side n.  Frank M Jackson, Dec 03 2014


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = A002620(n+1)A247588(n).  Frank M Jackson, Dec 03 2014


EXAMPLE

a(5)=3 as there are 3 noncongruent integer triangles with base length 5 whose apex lies on or within the space bounded by the semicircle of diameter 5. The integer triples are (2,4,5), (3,3,5), (3,4,5).


MATHEMATICA

sumtriangles[c_] := (n=0; Do[If[a^2+b^2<=c^2, n++], {b, 1, c}, {a, cb+1, b}]; n); Table[sumtriangles[m], {m, 1, 200}]


PROG

(PARI) a(n)=sum(a=2, n, sum(b=max(a, n+1a), n, a^2+b^2<=n^2)) \\ Charles R Greathouse IV, Mar 26 2014
(PARI) a(n)=sum(a=2, n, max(min(sqrtint(n^2a^2), n)max(a, n+1a)+1, 0)) \\ Charles R Greathouse IV, Mar 26 2014


CROSSREFS

Cf. A002620, A247588.
Sequence in context: A030502 A201025 A288451 * A073957 A309916 A162311
Adjacent sequences: A236381 A236382 A236383 * A236385 A236386 A236387


KEYWORD

nonn


AUTHOR

Frank M Jackson, Jan 24 2014


STATUS

approved



