|
|
A157440
|
|
a(n) = 121*n^2 - 204*n + 86.
|
|
3
|
|
|
3, 162, 563, 1206, 2091, 3218, 4587, 6198, 8051, 10146, 12483, 15062, 17883, 20946, 24251, 27798, 31587, 35618, 39891, 44406, 49163, 54162, 59403, 64886, 70611, 76578, 82787, 89238, 95931, 102866, 110043, 117462, 125123, 133026, 141171
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The identity (14641*n^2 - 24684*n + 10405)^2 - (121*n^2 - 204*n + 86)*(1331*n - 1122)^2 = 1 can be written as A157442(n)^2 - a(n)*A157441(n)^2 = 1. - Vincenzo Librandi, Jan 29 2012
The continued fraction expansion of sqrt(a(n)) is [11n-10; {1, 2, 1, 2, 11n-10, 2, 1, 2, 1, 22n-20}]. For n=1, this collapses to [1; {1, 2}]. - Magus K. Chu, Sep 13 2022
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
|
|
PROG
|
(Magma) I:=[3, 162, 563]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|