A246172 a(n) = (n^2+9*n-8)/2.

1, 7, 14, 22, 31, 41, 52, 64, 77, 91, 106, 122, 139, 157, 176, 196, 217, 239, 262, 286, 311, 337, 364, 392, 421, 451, 482, 514, 547, 581, 616, 652, 689, 727, 766, 806, 847, 889, 932, 976, 1021, 1067, 1114, 1162, 1211, 1261, 1312, 1364, 1417, 1471

Offset: 1

Author

Vincenzo Librandi, Aug 24 2014

Keywords

• nonn
• easy

Comments

a(n) - 7*(n-1) is a triangular number. Sequence gives positive x values solving the Diophantine equation y^2 - 8*x = 113. - Bruno Berselli, Aug 27 2014

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Magma

[(n^2+9*n-8)/2: n in [1..60]];

Mathematica

Table[(n^2 + 9 n - 8)/2, {n, 1, 60}]

PARI

a(n)=(n^2+9*n-8)/2 \\ Charles R Greathouse IV, Jun 17 2017

Sage

[(n^2+9*n-8)/2 for n in (1..60)] # Bruno Berselli, Aug 27 2014

Formula

G.f.: x*(1+4*x-4*x^2)/(1-x)^3.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) = 2*a(n-1)-a(n-2)+1.

a(n+1) - a(n) = n + 5. - Jacques ALARDET, Aug 04 2015

Sum_{n>=1} 1/a(n) = 4919/8008 + 2*Pi*tan(sqrt(113)*Pi/2)/sqrt(113). - Amiram Eldar, Feb 25 2023