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A082044 Main diagonal of A082043. 13
1, 4, 25, 100, 289, 676, 1369, 2500, 4225, 6724, 10201, 14884, 21025, 28900, 38809, 51076, 66049, 84100, 105625, 131044, 160801, 195364, 235225, 280900, 332929, 391876, 458329, 532900, 616225, 708964, 811801, 925444, 1050625, 1188100 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = longest side b of all integer-sided triangles with sides a<=b<=c and inradius n >= 1. Triangle has sides (n^2+2,n^4+2n^2+1,n^4+3n^2+1).

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = n^4+2n^2+1.

a(0)=1, a(1)=4, a(2)=25, a(3)=100, a(4)=289, a(n) = 5*a(n-1)-10*a(n-2)+ 10*a(n-3)- 5*a(n-4)+a(n-5). - Harvey P. Dale, Feb 27 2015

a(n) = (2*(2* A000217(n-1)^2 +(A002061(n)))^2 / A082044(n-1). - Bruce J. Nicholson, Apr 17 2017

a(n) = A002522(n)^2 = (n^2 + 1)^2 = a(-n) for all n in Z. - Michael Somos, Apr 17 2017

G.f.: (1 - x + 15*x^2 + 5*x^3 + 4*x^4 ) / (1 - x)^5. - Michael Somos, Apr 17 2017

EXAMPLE

G.f. = 1 + 4*x + 25*x^2 + 100*x^3 + 289*x^4 + 676*x^5 + 1369*x^6 + ...

MAPLE

seq(fibonacci(3, n)^2, n=0..33); # Zerinvary Lajos, Apr 09 2008

MATHEMATICA

Fibonacci[3, Range[0, 40]]^2 (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 25, 100, 289}, 40] (* Harvey P. Dale, Feb 27 2015 *)

PROG

(PARI) a(n) = n^4+2*n^2+1; \\ Michel Marcus, Jan 22 2016

CROSSREFS

Cf. A059826, A082047.

See A120062 for sequences related to integer-sided triangles with integer inradius n.

Cf. A002061, A000217, A002522.

Sequence in context: A264167 A152215 A231175 * A167889 A329495 A042651

Adjacent sequences:  A082041 A082042 A082043 * A082045 A082046 A082047

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 03 2003

STATUS

approved

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Last modified December 12 17:59 EST 2019. Contains 329960 sequences. (Running on oeis4.)