A177049 Numerator of (3n+1)*(3n+2)/4.

1, 5, 14, 55, 91, 68, 95, 253, 325, 203, 248, 595, 703, 410, 473, 1081, 1225, 689, 770, 1711, 1891, 1040, 1139, 2485, 2701, 1463, 1580, 3403, 3655, 1958, 2093, 4465, 4753, 2525, 2678, 5671, 5995, 3164, 3335, 7021, 7381, 3875, 4064, 8515, 8911

Offset: 0

Author

Paul Curtz, Dec 09 2010

Keywords

• nonn
• frac
• less
• easy

Comments

A trisection of A064038.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).

Crossrefs

Cf. A064038, A127922.

Programs

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 *)

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