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A189356
a(n) gives y-values solving the Diophantine equation 2*x^2 + (x-1)^2 = y^2 for positive x.
2
3, 41, 571, 7953, 110771, 1542841, 21489003, 299303201, 4168755811, 58063278153, 808717138331, 11263976658481, 156886956080403, 2185153408467161, 30435260762459851, 423908497265970753, 5904283700961130691, 82236063316189858921, 1145400602725696894203
OFFSET
1,1
COMMENTS
(a(n)-1)/2 gives indices of triangular numbers which are also pentagonal (A046175).
FORMULA
a(n) = 14*a(n-1) - a(n-2).
G.f.: x*(3-x)/(1-14*x+x^2). - Bruno Berselli, May 03 2011
MATHEMATICA
LinearRecurrence[{14, -1}, {3, 41}, 19] (* Bruno Berselli, Nov 11 2011 *)
PROG
(Magma) [n le 2 select 38*n-35 else 14*Self(n-1)-Self(n-2): n in [1..19]]; // Bruno Berselli, May 03 2011
CROSSREFS
KEYWORD
nonn
AUTHOR
Sture Sjöstedt, May 02 2011
EXTENSIONS
Extended by T. D. Noe, May 02 2011
STATUS
approved