OFFSET
1,2
COMMENTS
Equivalently, numbers of the form m*(14*m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of 2*h*(h+1)/7.
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.: 4*x^2*(3+x+3*x^2)/((1+x)^2*(1-x)^3).
a(n) = a(-n+1) = (14*n*(n-1)+5*(-1)^n*(2*n-1)+1)/4 +1.
a(n) = 2*A219191(n).
Sum_{n>=2} 1/a(n) = 7/2 - cot(Pi/7)*Pi/2. - Amiram Eldar, Mar 15 2022
MAPLE
A219390:=proc(q)
local n;
for n from 1 to q do if type(sqrt(14*n+1), integer) then print(n);
fi; od; end:
A219390(1000); # Paolo P. Lava, Feb 19 2013
MATHEMATICA
Select[Range[0, 7000], IntegerQ[Sqrt[14 # + 1]] &]
CoefficientList[Series[4 x (3 + x + 3 x^2) ((1 + x)^2 (1 - x)^3), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{1, 2, -2, -1, 1}, {0, 12, 16, 52, 60}, 50] (* Harvey P. Dale, Feb 05 2019 *)
PROG
(Magma) [n: n in [0..7000] | IsSquare(14*n+1)];
(Magma) I:=[0, 12, 16, 52, 60]; [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