A048759 Longest perimeter of a Pythagorean triangle with n as length of one of the three sides.

12, 12, 30, 24, 56, 40, 90, 60, 132, 84, 182, 112, 240, 144, 306, 180, 380, 220, 462, 264, 552, 312, 650, 364, 756, 420, 870, 480, 992, 544, 1122, 612, 1260, 684, 1406, 760, 1560, 840, 1722, 924, 1892, 1012, 2070, 1104, 2256, 1200, 2450, 1300, 2652

Offset: 3

Author

Henry Bottomley, Jun 15 2000

Keywords

• nonn
• easy

Links

• Stefano Spezia, Table of n, a(n) for n = 3..10000
• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A010814, A029578, A055522, A055523, A055524.

Programs

Magma

[(3*n^2+4*n-n^2*(-1)^n)/4: n in [3..60]]; // Vincenzo Librandi, Jul 19 2015

Mathematica

A048759[n_] := (3 - (-1)^n)*n^2 / 4 + n; Array[A048759, 100, 3] (* or *)
LinearRecurrence[{0, 3, 0, -3, 0, 1}, {12, 12, 30, 24, 56, 40}, 100] (* Paolo Xausa, Feb 29 2024 *)

PARI

Vec(-2*x^3*(2*x^5+x^4-6*x^3-3*x^2+6*x+6)/((x-1)^3*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 13 2014

Formula

a(n) = n*A029578(n+2) = n+A055523(n)+A055524(n).

a(2*k) = 2*k*(k+1), a(2*k+1) = 2*(2*k+1)*(k+1).

a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). - Colin Barker, Sep 13 2014

G.f.: -2*x^3*(2*x^5+x^4-6*x^3-3*x^2+6*x+6) / ((x-1)^3*(x+1)^3). - Colin Barker, Sep 13 2014

a(n) = (3*n^2+4*n-n^2*(-1)^n)/4. - Luce ETIENNE, Jul 18 2015

E.g.f.: x*((4 + x)*cosh(x) + (3 + 2*x)*sinh(x) - 4*(1 + x))/2. - Stefano Spezia, May 24 2021