|
|
A127262
|
|
a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 12*a(n-2).
|
|
2
|
|
|
2, 2, 28, 80, 496, 1952, 9856, 43136, 204544, 926720, 4307968, 19736576, 91168768, 419176448, 1932378112, 8894873600, 40978284544, 188695052288, 869129519104, 4002599665664, 18434753560576, 84900703109120
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
If A091914(n-1)=F(n) the Fibonacci-like sequence, then a(n) is the Lucas-type sequence.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = ((1+sqrt(13))^n - (1-sqrt(13)^n))/(2*sqrt(13)).
G.f.: 2*(1-x)/(1-2*x-12*x^2).
E.g.f.: exp((1+sqrt(13))*x) + exp((1-sqrt(13))*x).
|
|
MAPLE
|
a[0]:=2:a[1]:=2:for i from 2 to 40 do a[i]:=2*a[i-1]+12*a[i-2] od: seq(a[n], n=0..40);
|
|
MATHEMATICA
|
LinearRecurrence[{2, 12}, {2, 2}, 30] (* Harvey P. Dale, May 24 2017 *)
|
|
PROG
|
(Sage) [lucas_number2(n, 2, -12) for n in range(0, 22)] # Zerinvary Lajos, Apr 30 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|