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A157442
a(n) = 14641*n^2 - 24684*n + 10405.
3
362, 19601, 68122, 145925, 253010, 389377, 555026, 749957, 974170, 1227665, 1510442, 1822501, 2163842, 2534465, 2934370, 3363557, 3822026, 4309777, 4826810, 5373125, 5948722, 6553601, 7187762, 7851205, 8543930, 9265937
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 a(n)^2 - A157440(n)*A157441(n)^2 = 1. - Vincenzo Librandi, Jan 29 2012
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=362, a(2)=19601, a(3)=68122. - Harvey P. Dale, Oct 22 2011
G.f.: x*(-10405*x^2 - 18515*x - 362)/(x-1)^3. - Harvey P. Dale, Oct 22 2011
a(n) = A017485(11*n-10)^2 + 1. - Bruno Berselli, Jan 29 2012
MATHEMATICA
Table[14641n^2-24684n+10405, {n, 30}] (* or *) LinearRecurrence[{3, -3, 1}, {362, 19601, 68122}, 30]
PROG
(Magma) I:=[362, 19601, 68122]; [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
(PARI) for(n=1, 40, print1(14641*n^2 - 24684*n + 10405", ")); \\ Vincenzo Librandi, Jan 29 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
STATUS
approved