|
|
A115598
|
|
Consider all Pythagorean triples (X,X+1,Z) ordered by increasing Z; sequence gives Z-(X+1) values.
|
|
4
|
|
|
1, 8, 49, 288, 1681, 9800, 57121, 332928, 1940449, 11309768, 65918161, 384199200, 2239277041, 13051463048, 76069501249, 443365544448, 2584123765441, 15061377048200, 87784138523761, 511643454094368, 2982076586042449, 17380816062160328, 101302819786919521
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = (-2+(3-2*sqrt(2))^n+(3+2*sqrt(2))^n)/4.
a(n) = 7*a(n-1)-7*a(n-2)+a(n-3).
G.f.: -x*(x+1) / ((x-1)*(x^2-6*x+1)).
|
|
MATHEMATICA
|
LinearRecurrence[{7, -7, 1}, {1, 8, 49}, 30] (* Harvey P. Dale, Oct 27 2013 *)
CoefficientList[Series[-(x + 1)/((x - 1) (x^2 - 6 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 28 2014 *)
|
|
CROSSREFS
|
Essentially a duplicate of A001108.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|