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A145820 Numbers n such that 17, n, n+1 are the sides of a Heron triangle, i.e., a triangle with integer sides and integer area. 2
8, 9, 16, 25, 40, 89, 144, 233, 520, 841, 1360, 3033, 4904, 7929, 17680, 28585, 46216, 103049, 166608, 269369, 600616, 971065, 1570000, 3500649, 5659784, 9150633, 20403280, 32987641, 53333800, 118919033, 192266064, 310852169, 693110920 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers n such that the square root of 72*(n-8)*(n+9) is an integer. - Harvey P. Dale, Jun 23 2013

LINKS

Table of n, a(n) for n=1..33.

FORMULA

a(n) = a(n-1) + 6*a(n-3) - 6*a(n-4) - a(n-6) + a(n-7), with a(1)=8, a(2)=9, a(3)=16, a(4)=25, a(5)=40, a(6)=89, a(7)=144

G.f.: (-9*x^6 - 7*x^5 - 9*x^4 + 39*x^3 - 7*x^2 - x - 8)/(x^7 - x^6 - 6*x^4 + 6*x^3 + x - 1).

EXAMPLE

For n=2 the triangle has sides 17,9,10 with area 36.

MAPLE

A145820 := proc (n) local L; option remember;

L := [8, 9, 16, 25, 40, 89, 144];

if n < 8 then L[n] else A145820(n-1)+6*A145820(n-3)-6*A145820(n-4)-A145820(n-6)+A145820(n-7) end if;

end proc;

seq(A145820(n), n=1..50);

MATHEMATICA

LinearRecurrence[{1, 0, 6, -6, 0, -1, 1}, {8, 9, 16, 25, 40, 89, 144}, 40] (* Harvey P. Dale, Jun 23 2013 *)

CROSSREFS

Cf. A145821.

Sequence in context: A192636 A265731 A227646 * A227647 A175053 A274406

Adjacent sequences:  A145817 A145818 A145819 * A145821 A145822 A145823

KEYWORD

nonn

AUTHOR

James R. Buddenhagen, Oct 20 2008

STATUS

approved

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Last modified June 19 17:44 EDT 2019. Contains 324222 sequences. (Running on oeis4.)