|
|
A055523
|
|
Longest other leg of a Pythagorean triangle with n as length of a leg.
|
|
12
|
|
|
4, 3, 12, 8, 24, 15, 40, 24, 60, 35, 84, 48, 112, 63, 144, 80, 180, 99, 220, 120, 264, 143, 312, 168, 364, 195, 420, 224, 480, 255, 544, 288, 612, 323, 684, 360, 760, 399, 840, 440, 924, 483, 1012, 528, 1104, 575, 1200, 624, 1300, 675, 1404, 728, 1512, 783
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,1
|
|
LINKS
|
|
|
FORMULA
|
a(2k) = (k-1)*(k+1), a(2k+1) = 2k*(k+1).
a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: x^3*(x^3-3*x-4) / ((x-1)^3*(x+1)^3). - Colin Barker, Sep 15 2014
a(n) = (3*(n^2-2)+(-1)^(n+1)*(n^2+2))/8. - Todd Silvestri, Dec 16 2014
E.g.f.: 1 + (3*x^2/8 + 3*x/8 - 3/4)*exp(x) + (-x^2/8 + x/8 - 1/4)*exp(-x). - Robert Israel, Dec 16 2014
|
|
MAPLE
|
seq(`if`(n::even, (n/2-1)*(n/2+1), (n-1)*(n+1)/2), n=3..100); # Robert Israel, Dec 16 2014
|
|
MATHEMATICA
|
a[n_Integer/; n>=3]:=(3 (n^2-2)+(-1)^(n+1) (n^2+2))/8 (* Todd Silvestri, Dec 16 2014 *)
|
|
PROG
|
(PARI) Vec(x^3*(x^3-3*x-4)/((x-1)^3*(x+1)^3) + O(x^100)) \\ Colin Barker, Sep 15 2014
|
|
CROSSREFS
|
Cf. A009112, A046079, A046080, A046081, A054435, A054436, A055522, A055524, A055525, A055526, A055527.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|