OFFSET
1,1
COMMENTS
Positive numbers k such that k^2 == 2 (mod 151), where the prime 151 == -1 (mod 8).
Equivalently, numbers k such that k == 46 or 105 (mod 151). - Bruno Berselli, Mar 08 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
G.f.: x*(46+59*x+46*x^2)/((1+x)*(x-1)^2).
a(n) = (-151-33*(-1)^n+302*n)/4.
a(n) = a(n-1) +a(n-2) -a(n-3).
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(59*Pi/302)*Pi/151. - Amiram Eldar, Feb 28 2023
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {46, 105, 197}, 40] (* or *) CoefficientList[Series[x*(46+59*x+46*x^2)/((1+x)*(x-1)^2), {x, 0, 33}], x] (* or *) a[1] = 46; a[n_] := a[n] = 151*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]
PROG
(Magma) [(-151-33*(-1)^n+302*n)/4: n in [1..60]];
(PARI) a(n)=(-151-33*(-1)^n+302*n)/4 \\ Charles R Greathouse IV, Oct 16 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 08 2012
STATUS
approved