|
|
A187361
|
|
Pell trisection: Pell(3*n+1), n >= 0.
|
|
2
|
|
|
1, 12, 169, 2378, 33461, 470832, 6625109, 93222358, 1311738121, 18457556052, 259717522849, 3654502875938, 51422757785981, 723573111879672, 10181446324101389, 143263821649299118, 2015874949414289041, 28365513113449345692, 399133058537705128729, 5616228332641321147898
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
For the general computation of the o.g.f.s for the trisection of a sequence, given by its real o.g.f., see a Wolfdieter Lang comment under A187357.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Pell(3*n+1), n >= 0, with Pell(n):=A000129(n).
O.g.f.: (1-2*x)/(1-14*x-x^2).
a(n) = 14*a(n-1) + a(n-2), a(0)= 1, a(1)=12.
a(n) = (((7-5*sqrt(2))^n*(-1+sqrt(2))+(1+sqrt(2))*(7+5*sqrt(2))^n))/(2*sqrt(2)). - Colin Barker, Jan 25 2016
|
|
MATHEMATICA
|
LinearRecurrence[{14, 1}, {1, 12}, 20] (* Harvey P. Dale, Jul 06 2023 *)
|
|
PROG
|
(PARI) Vec((1-2*x)/(1-14*x-x^2) + O(x^20)) \\ Colin Barker, Jan 25 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|