OFFSET
0,2
COMMENTS
Numbers m such that r = 24*m+1 and 2*r-1 are both squares. - Bruno Berselli, Jul 17 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (35,-35,1).
FORMULA
From Colin Barker, Mar 02 2016: (Start)
a(n) = 35*a(n-1) - 35*a(n-2) + a(n-3) for n > 2.
a(n) = ( (99-70*sqrt(2))*(17-12*sqrt(2))^n - 6 + (99+70*sqrt(2))*(17+12*sqrt(2))^n )/192. (End)
a(n) = ( Pell(2*n+3)^2 - 1)/24 = (Q(4*n+6) - 6)/192, where Q(n) = Pell-Lucas numbers. - G. C. Greubel, Jan 13 2020
MAPLE
seq(coeff(series(1/( (1-x)*(1-34*x+x^2) ), x, n+1), x, n), n = 0..20); # G. C. Greubel, Jan 13 2020
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {1, 35, 1190}, 20] (* Vincenzo Librandi, Nov 22 2011 *)
Table[(Fibonacci[2*n+3, 2]^2 -1)/24, {n, 0, 20}] (* G. C. Greubel, Jan 13 2020 *)
PROG
(Magma) I:=[1, 35, 1190]; [n le 3 select I[n] else 35*Self(n-1)-35*Self(n-2) +Self(n-3): n in [1..20]]; // Vincenzo Librandi, Nov 22 2011
(PARI) Vec(1/(1-35*x+35*x^2-x^3)+O(x^20)) \\ Charles R Greathouse IV, Sep 23 2012
(Sage) [(lucas_number2(4*n+6, 2, -1) -6)/192 for n in (0..20)] # G. C. Greubel, Jan 13 2020
(GAP) List([0..20], n-> (Lucas(2, -1, 4*n+6)[2] -6)/192 ); # G. C. Greubel, Jan 13 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved