OFFSET
0,2
COMMENTS
REFERENCES
T. Bier, Classifications of solutions of certain positive biquadratic division system, submitted May 12 2014.
T. Bier and O. Dira, Construction of integer sequences, submitted May 12 2014.
LINKS
Oboifeng Dira, Sequences solving division systems
Index entries for linear recurrences with constant coefficients, signature (4,0,-4,1).
FORMULA
a(n+1) = 4*a(n) - a(n-1) - p_n (n>0), where p_n=0 if n is odd and p_n = 1 if n is even.
a(n) = 4*a(n-1) - 4*a(n-3) + a(n-4). - Colin Barker, May 21 2014
G.f.: -(x^3-x^2-2*x+1) / ((x-1)*(x+1)*(x^2-4*x+1)). - Colin Barker, May 21 2014
a(n) = (1/12) * (2*A077136(n) + (-1)^n + 3). - Ralf Stephan, May 24 2014
EXAMPLE
Considering the pair a(1)=2 and a(2)=7, 2 divides 7^2+1 and 7 divides 2^2+2+1.
MAPLE
x0:=1: x1:=2: L:=[x0, x1]: for k from 1 to 30 do:if k mod 2 = 1 then z:=4*x1-x0: fi: if k mod 2 = 0 then z:=4*x1-x0-1: fi: L:=[op(L), z]: x0:=x1: x1:=z: od: print(L);
PROG
(PARI) Vec(-x*(x^3-x^2-2*x+1)/((x-1)*(x+1)*(x^2-4*x+1)) + O(x^100)) \\ Colin Barker, May 21 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Oboifeng Dira, May 21 2014
STATUS
approved