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A048759 Longest perimeter of a Pythagorean triangle with n as length of one of the three sides. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
LINKS
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
Sequence in context: A251643 A346531 A070710 * A364434 A303646 A298036
KEYWORD
nonn,easy
AUTHOR
Henry Bottomley, Jun 15 2000
STATUS
approved

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Last modified June 18 07:40 EDT 2024. Contains 373469 sequences. (Running on oeis4.)