OFFSET
0,2
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (I).
Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (II).
Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (III).
Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (IV).
Index entries for linear recurrences with constant coefficients, signature (11,-11,1).
FORMULA
G.f.: 4*x/(1-11*x+11*x^2-x^3).
a(0)=0, a(1)=4, a(2)=44, a(n)=11*a(n-1)-11*a(n-2)+a(n-3). - Harvey P. Dale, Sep 29 2013
a(n) = (-6-(5-2*sqrt(6))^n*(-3+sqrt(6))+(3+sqrt(6))*(5+2*sqrt(6))^n)/12. - Colin Barker, Mar 05 2016
a(n) = (A072256(n+1) - 1)/2.
MATHEMATICA
CoefficientList[Series[4x/(1-11x+11x^2-x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{11, -11, 1}, {0, 4, 44}, 30] (* Harvey P. Dale, Sep 29 2013 *)
PROG
(PARI) for(n=0, 427284, if(issquare(6*n*(n+1)+1), print1(n, ", ")))
(PARI) Vec(4*x/(1-11*x+11*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Nov 13 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gerald McGarvey, Apr 03 2005
EXTENSIONS
More terms from Vladeta Jovovic, Apr 05 2005
Incorrect conjectures deleted by N. J. A. Sloane, Nov 24 2010
STATUS
approved