

A057721


n^4 + 3*n^2 + 1.


9



1, 5, 29, 109, 305, 701, 1405, 2549, 4289, 6805, 10301, 15005, 21169, 29069, 39005, 51301, 66305, 84389, 105949, 131405, 161201, 195805, 235709, 281429, 333505, 392501, 459005, 533629, 617009, 709805, 812701, 926405, 1051649
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OFFSET

0,2


COMMENTS

Longest possible side c of a triangle with integer sides a<=b<c and inradius n. Triangle has sides (n^2+2,n^4+2n^2+1,n^4+3n^2+1). Proved by Joseph Myers, Jun 11 2006.


LINKS

Table of n, a(n) for n=0..32.
Michelle RudolphLilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894, 2015
Index entries for linear recurrences with constant coefficients, signature (5, 10, 10, 5, 1).


FORMULA

a(n) = Denominator of Integral(sin(n*x)/(exp((n^2+1)*x)),x=0..infinity). [Francesco Daddi, Jul 07 2013]


MAPLE

with(combinat, fibonacci):seq(fibonacci(5, i), i=0..32);  Zerinvary Lajos, Dec 01 2006


MATHEMATICA

Table[Fibonacci[5, i], {i, 0, 40}]; ..and/or..f[n_]:=n^4+3n^2+1; Array[f, 40, 0] (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)


PROG

(Sage) [lucas_number1(5, n, 1) for n in xrange(0, 33)] # Zerinvary Lajos, May 16 2009


CROSSREFS

See A120062 for sequences related to integersided triangles with integer inradius n.
Cf. A120062 [triangles with integer inradius], A120063 [minimum of their longest sides].
Sequence in context: A097344 A153076 A034700 * A085151 A119494 A268929
Adjacent sequences: A057718 A057719 A057720 * A057722 A057723 A057724


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 27 2000


STATUS

approved



