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

3,1

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).

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A251643 A346531 A070710 * A364434 A303646 A298036

Adjacent sequences: A048756 A048757 A048758 * A048760 A048761 A048762

Keyword

nonn,easy

Author

Henry Bottomley, Jun 15 2000

Status

approved