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A048759 Longest perimeter of a Pythagorean triangle with n as length of one of the three sides. 1
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

Table of n, a(n) for n=3..51.

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

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, A055522.

Sequence in context: A299853 A251643 A070710 * A303646 A298036 A119877

Adjacent sequences:  A048756 A048757 A048758 * A048760 A048761 A048762

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Jun 15 2000

STATUS

approved

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Last modified October 18 03:25 EDT 2019. Contains 328135 sequences. (Running on oeis4.)