OFFSET
1,2
LINKS
Colin Barker, Table of n, a(n) for n = 1..400
Index entries for linear recurrences with constant coefficients, signature (195,-195,1).
FORMULA
a(n) = (A001570(n)^2 - 1)/3.
G.f.: 56*x^2 / (1-195*x+195*x^2-x^3).
From Colin Barker, Mar 03 2016: (Start)
a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n>3.
a(n) = (-1)*((97+56*sqrt(3))^(-n)*(-1+(97+56*sqrt(3))^n)*(7+4*sqrt(3)+(-7+4*sqrt(3))*(97+56*sqrt(3))^n))/48.
(End)
EXAMPLE
3*56+1=13^2 and 4*56+1=15^2.
MAPLE
f:= proc(n) local u;
u:= <<7, 8>|<6, 7>>^n . <1, -1>;
(u[1]^2-1)/3
end proc:
map(f, [$1..30]); # Robert Israel, Mar 03 2016
MATHEMATICA
CoefficientList[Series[56 x/(1 - 195 x + 195 x^2 - x^3), {x, 0, 13}], x] (* Michael De Vlieger, Mar 03 2016 *)
PROG
(PARI) isok(n) = issquare(3*n+1) && issquare(4*n+1) \\ Michel Marcus, Jun 08 2013
(PARI) concat(0, Vec(56*x^2/((1-x)*(1-194*x+x^2)) + O(x^20))) \\ Colin Barker, Mar 03 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
David Radcliffe, Mar 07 2001
EXTENSIONS
Offset changed to 1 by Joerg Arndt, Mar 03 2016
STATUS
approved