OFFSET
1,1
COMMENTS
Square roots of resulting squares gives A001651. - Ray Chandler, Apr 14 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
From Ilya Gutkovskiy, Apr 13 2016: (Start)
G.f.: x*(3 + x - 2*x^2 + x^3 + 3*x^4)/((1 - x)^3*(1 + x)^2).
a(n) = (6*(n - 1)*n - (2*n - 1)*(-1)^n + 23)/8. (End)
EXAMPLE
a(1) = 3 because 3*3 - 8 = 1^2.
MAPLE
seq(seq(((3*m+k)^2+8)/3, k=1..2), m=0..50); # Robert Israel, Dec 05 2016
MATHEMATICA
Select[Range@ 2400, IntegerQ@ Sqrt[3 # - 8] &] (* Bruno Berselli, Apr 14 2016 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {3, 4, 8, 11, 19}, 60] (* Harvey P. Dale, Oct 02 2020 *)
PROG
(Magma) [n: n in [1..2400] | IsSquare(3*n-8)];
(Python) from gmpy2 import is_square
[n for n in range(3000) if is_square(3*n-8)] # Bruno Berselli, Dec 05 2016
(Python) [(6*(n-1)*n-(2*n-1)*(-1)**n+23)/8 for n in range(1, 60)] # Bruno Berselli, Dec 05 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Juri-Stepan Gerasimov, Apr 13 2016
STATUS
approved