reviewed
approved
reviewed
approved
proposed
reviewed
editing
proposed
Sequences of numbers of the form n*(n*k - k + 6)/2:
0, 3, 17, 42, 78, 125, 183, 252, 332, 423, 525, 638, 762, 897, 1043, 1200, 1368, 1547, 1737, 1938, 2150, 2373, 2607, 2852, 3108, 3375, 3653, 3942, 4242, 4553, 4875, 5208, 5552, 5907, 6273, 6650, 7038, 7437, 7847, 8268, 8700, 9143, 9597, 10062, 10538, 11025, 11523
Sum of reciprocals of a(n), for n > 0: 0.47118857003113149692081665034891...
From Elmo R. Oliveira, Dec 27 2024: (Start)
E.g.f.: exp(x)*x*(6 + 11*x)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
a(n) = n + A180223(n). (End)
approved
editing
(MAGMAMagma) [n*(11*n-5)/2: n in [0..50]];
(MAGMAMagma) I:=[0, 3, 17]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..46]]; // Vincenzo Librandi, Aug 18 2013
editing
approved
LinearRecurrence[{3, -3, 1}, {0, 3, 17}, 50] (* Harvey P. Dale, Jan 14 2019 *)
approved
editing
editing
approved
(PARI) a(n)=n*(11*n-5)/2 \\ Charles R Greathouse IV, Sep 24 2015
approved
editing