OFFSET
1,1
COMMENTS
It is conjectured that A003325 and A052276 (the current sequence) have infinitely many numbers in common, although only one example (128) is known.
The next such example must be larger than 2*10^12. - M. F. Hasler, Jan 10 2021
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = a(n-1)+3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7) for n>8. - Colin Barker, Jul 09 2015
G.f.: x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3) / ((x-1)^4*(x+1)^3). - Colin Barker, Jul 09 2015
a(n) = ((2*n+1)*(n^2+n+1) - (-1)^n*(3*n^2+3*n-47))/16 for n >= 2. - Robert Israel, Jul 09 2015
a(n) = ceiling(n/2)^3 + 3*(-1)^n for all n > 1. - M. F. Hasler, Jan 10 2021
MAPLE
3, 4, op(map(n -> (n^3-3, n^3+3), [$2..100])); # Robert Israel, Jul 09 2015
PROG
(PARI) Vec(x*(5*x^7-8*x^6-9*x^5+19*x^4+3*x^3-8*x^2+x+3)/((x-1)^4*(x+1)^3) + O(x^100)) \\ Colin Barker, Jul 09 2015
(PARI) apply( {A052276(n)=(n\/2)^3+3*(-1)^n+(n==1)*5}, [1..99]) \\ M. F. Hasler, Jan 10 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Feb 05 2000
STATUS
approved