OFFSET
0,2
COMMENTS
Numbers h such that 6*h+1 and 8*h+1 are both squares. - Bruno Berselli, Jul 07 2014
LINKS
Colin Barker, Table of n, a(n) for n = 0..400
Index entries for linear recurrences with constant coefficients, signature (195,-195,1).
FORMULA
For n > 1, a(n) = 194*a(n-1) - a (n-2) + 28. See A200998 for generalization.
From Colin Barker, Mar 02 2016: (Start)
a(n) = ((97+56*sqrt(3))^(-n)*(-1+(97+56*sqrt(3))^n)*(-7+4*sqrt(3)+(7+4*sqrt(3))*(97+56*sqrt(3))^n))/96.
a(n) = 195*a(n-1)-195*a(n-2)+a(n-3) for n > 2.
G.f.: 28*x / ((1-x)*(1-194*x+x^2)). (End)
Sum_{n>=1} 1/a(n) = (7 - 4*sqrt(3))/2 = A379338 - 1/2. - Amiram Eldar, Jan 27 2026
EXAMPLE
3*0 = 4*0.
3*28 = 4*21.
3*5640 = 4*4095.
3*1059240 = 4*794430.
MATHEMATICA
LinearRecurrence[{195, -195, 1}, {0, 28, 5460}, 20] (* T. D. Noe, Feb 15 2012 *)
PROG
(PARI) concat(0, Vec(28*x/((1-x)*(1-194*x+x^2)) + O(x^15))) \\ Colin Barker, Mar 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charlie Marion, Feb 15 2012
STATUS
approved