OFFSET
0,3
COMMENTS
Numbers with the property a(n)^2+a(n-1)^2 = 2*(a(n)-a(n-1)-(-1)^n)^2.
REFERENCES
R. C. Alperin, A family of nonlinear recurrences and their linear solutions, Fib. Q., 57:4 (2019), 318-321.
R. C. Alperin, A nonlinear recurrence and its relations to Chebyshev polynomials, Fib. Q., 58:2 (2020), 140-142.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,3,-1).
FORMULA
EXAMPLE
a(3)=23, a(2)=7: 23^2+7^2 = 2*(23-7-(-1)^3)^2 = 578;
a(6)=1231, a(5)=329: 1231^2+329^2 = 2*(1231-329-(-1)^6)^2 = 1623602.
MATHEMATICA
CoefficientList[Series[(1 - 2 x + x^2)/(1 - 3 x - 3 x^2 + x^3), {x, 0, 25}], x]
PROG
(PARI) Vec((1-2*x+x^2)/(1-3*x-3*x^2+x^3)+O(x^26))
(Magma) m:=26; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-2*x+x^2)/(1-3*x-3*x^2+x^3)));
(Maxima) makelist(coeff(taylor((1-2*x+x^2)/(1-3*x-3*x^2+x^3), x, 0, n), x, n), n, 0, 25);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Sep 28 2012
STATUS
approved