OFFSET
1,3
COMMENTS
This sequence is also the integers k such that x^6 - 8*k*x^4 - 1 is reducible over the integers, and, for k > 0 such that the factors are two irreducible cubics. - James R. Buddenhagen, May 29 2010
Integer solutions of x + y = (x - y)^4. If x = a(n) then y = a(n - (-1)^n). - Thomas Scheuerle, Mar 06 2023
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).
FORMULA
G.f.: -x^2*(x^4+6*x^3-2*x^2+6*x+1) / ((x-1)^5*(x+1)^4). - Colin Barker, Apr 28 2015
From Robert Israel, Apr 28 2015: (Start)
a(n) = (2*n^4 + 4*n^3 + 6*n^2 + 4*n - 7)/64 + (-1)^n * (7 - 2*n - 2*n^2)*(1 + 2*n)/64.
a(n+8) - 4*a(n+6) + 6*a(n+4) - 4*a(n+2) + a(n) = 12. (End)
MAPLE
map(k -> (k*(k^3-1)/2, k*(k^3+1)/2), [$1..100]); # Robert Israel, Apr 28 2015
PROG
(PARI) concat(0, Vec(-x^2*(x^4+6*x^3-2*x^2+6*x+1)/((x-1)^5*(x+1)^4) + O(x^100))) \\ Colin Barker, Apr 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 05 2000
STATUS
approved