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A289156 Largest area of triangles with integer sides and area = n times perimeter. 3
60, 1224, 8436, 34320, 103020, 254040, 546084, 1060896, 1907100, 3224040, 5185620, 8004144, 11934156, 17276280, 24381060, 33652800, 45553404, 60606216, 79399860, 102592080, 130913580, 165171864, 206255076, 255135840 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Ray Chandler, Table of n, a(n) for n = 1..5000 (first 100 terms from Zhining Yang)

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

From Colin Barker, Jun 28 2017: (Start)

G.f.: 12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6.

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

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

a(n) = A120573(2n). - Ray Chandler, Jul 27 2017

EXAMPLE

For n = 4, a(4) = 34320 means for the largest triangles (a,b,c) = (66,4225,4289), the area is 34320 which is 4 times the perimeter 8580.

MATHEMATICA

Table[4 n (2 n^2 + 1) (4 n^2 + 1), {n, 27}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {60, 1224, 8436, 34320, 103020, 254040}, 27] (* or *) Rest@ CoefficientList[Series[12 x (5 + 72 x + 166 x^2 + 72 x^3 + 5 x^4)/(1 - x)^6, {x, 0, 27}], x] (* Michael De Vlieger, Jul 03 2017 *)

PROG

(PARI) Vec(12*x*(5 + 72*x + 166*x^2 + 72*x^3 + 5*x^4) / (1 - x)^6 + O(x^30)) \\ Colin Barker, Jun 28 2017

CROSSREFS

Cf. A007237, A120573, A188158, A228383, A289155.

Sequence in context: A105252 A269138 A146347 * A288960 A269196 A054331

Adjacent sequences:  A289153 A289154 A289155 * A289157 A289158 A289159

KEYWORD

nonn,easy

AUTHOR

Zhining Yang, Jun 26 2017

STATUS

approved

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Last modified April 16 07:59 EDT 2021. Contains 343030 sequences. (Running on oeis4.)