OFFSET
0,2
COMMENTS
A trisection of A064038.
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).
FORMULA
Conjecture: a(n)= +3*a(n-1) -6*a(n-2) +10*a(n-3) -12*a(n-4) +12*a(n-5) -10*a(n-6) +6*a(n-7) -3*a(n-8) +a(n-9) with g.f. -(x^2+4*x+1)*(x^6-2*x^5+12*x^4-13*x^3+12*x^2-2*x+1) / ( (x-1)^3*(x^2+1)^3 ). - R. J. Mathar, Dec 12 2010
The conjecture is correct. - Charles R Greathouse IV, Feb 08 2012
a(n) ~ -27/8*n^2 - 27/8*n. - Ralf Stephan, Jun 16 2014
Sum_{n>=0} 1/a(n) = (4/(3*sqrt(3)) - 1/3)*Pi. - Amiram Eldar, Aug 13 2022
MATHEMATICA
Table[Numerator[(3 n + 1) (3 n + 2)/4], {n, 0, 50}] (* Wesley Ivan Hurt, Jun 14 2014 *)
LinearRecurrence[{3, -6, 10, -12, 12, -10, 6, -3, 1}, {1, 5, 14, 55, 91, 68, 95, 253, 325}, 50] (* Harvey P. Dale, Jan 18 2020 *)
CROSSREFS
KEYWORD
nonn,frac,less,easy
AUTHOR
Paul Curtz, Dec 09 2010
STATUS
approved