|
Search: id:A105037
|
|
|
| A105037 |
|
a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98, for n>3 a(n) = 22*a(n-2) - a(n-4) + 10. |
|
+0
3
|
|
| 0, 4, 6, 98, 142, 2162, 3128, 47476, 68684, 1042320, 1507930, 22883574, 33105786, 502396318, 726819372, 11029835432, 15956920408, 242153983196, 350325429614, 5316357794890, 7691202531110, 116717717504394, 168856130254816
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
It appears this sequence gives all nonnegative m such that 120*m^2 + 120*m + 1 is a square.
|
|
FORMULA
|
G.f.:-2*x*(2*x^2+x+2)/((x-1)*(x^4-22*x^2+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
a(n)=-1/2-1/5*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(-1)^n*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2 *sqrt(30))^(-1/4)*sqrt(30) + 5/4*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(11 + 2*sqrt(30))^(1/2 *n)*(11 + 2*sqrt(30))^(-1/4) + 5/24*(11 + 2*sqrt(30))^(1/4*(-1)^n)*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2*sqrt(30))^(-1/4)*sqrt(30)-5/24*(11-2*sqrt(30))^(-1/4)*sqrt(30)*(11-2 *sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n) + 5/4*(11-2*sqrt(30))^(-1/4)*(11-2 *sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n)-(11 + 2*sqrt(30))^(1/4*(-1)^n)*( -1)^n*(11 + 2*sqrt(30))^(1/2*n)*(11 + 2*sqrt(30))^(-1/4) + 1/5*(-1)^n*(11-2 *sqrt(30))^(-1/4)*sqrt(30)*(11-2*sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n) -(-1)^n*(11-2*sqrt(30))^(-1/4)*(11-2*sqrt(30))^(1/4*(-1)^n)*(11-2*sqrt(30))^(1/2*n), with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 28 2009]
|
|
CROSSREFS
|
Sequence in context: A013079 A087934 A052684 this_sequence A139730 A013023 A012909
Adjacent sequences: A105034 A105035 A105036 this_sequence A105038 A105039 A105040
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Apr 03 2005
|
|
|
Search completed in 0.002 seconds
|
