OFFSET
1,2
COMMENTS
Equivalently, numbers of the form m*(27*m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of h*(h+2)/27.
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).
FORMULA
G.f.: x^2*(25 + 4*x + 25*x^2)/((1 + x)^2*(1 - x)^3).
a(n) = a(-n+1) = (54*n*(n-1) + 23*(-1)^n*(2*n - 1) - 1)/8 + 3.
Sum_{n>=2} 1/a(n) = 27/4 - cot(2*Pi/27)*Pi/2. - Amiram Eldar, Mar 17 2022
MAPLE
A219258:=proc(q)
local n;
for n from 1 to q do if type(sqrt(27*n+1), integer) then print(n);
fi; od; end:
A219258(1000); # Paolo P. Lava, Feb 19 2013
MATHEMATICA
Select[Range[0, 14000], IntegerQ[Sqrt[27 # + 1]] &]
CoefficientList[Series[x (25 + 4 x + 25 x^2)/((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *)
PROG
(Magma) [n: n in [0..14000] | IsSquare(27*n+1)];
(Magma) I:=[0, 25, 29, 104, 112]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Nov 19 2012
STATUS
approved