OFFSET
4,1
COMMENTS
The members of each quartet are related by the Diophantine formula,
( (4*k-3)^2+(4*k-2)^2 ) * ( (4*k-1)^2+(4*k)^2 ) = a(4*k)^2 + a(4*k+1)^2 = a(4*k+2)^2 + a(4*k+3)^2 .
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,-1,1,2,-2,2,-2,-1,1,-1,1).
FORMULA
a(n) = a(n-1) -a(n-2) +a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-6) -2*a(n-7) -a(n-8) +a(n-9) -a(n-10) +a(n-11).
G.f.: x^4* (-2-9*x-x^2-4*x^3+8*x^4-58*x^5+6*x^6+2*x^8-5*x^9+3*x^10-4*x^7)/( (1+x)^2 * (x-1)^3 * (x^2+1)^3 ).
EXAMPLE
k=1 contributes the quartet (2,11,10,5). k=2 contributes (2,83,82,13) etc.
CROSSREFS
KEYWORD
nonn,less,easy
AUTHOR
Juri-Stepan Gerasimov, Jun 26 2009
EXTENSIONS
Edited and corrected by R. J. Mathar, Oct 04 2009
STATUS
approved