A226490 a(n) = n*(19*n-15)/2.

0, 2, 23, 63, 122, 200, 297, 413, 548, 702, 875, 1067, 1278, 1508, 1757, 2025, 2312, 2618, 2943, 3287, 3650, 4032, 4433, 4853, 5292, 5750, 6227, 6723, 7238, 7772, 8325, 8897, 9488, 10098, 10727, 11375, 12042, 12728, 13433, 14157, 14900, 15662, 16443, 17243, 18062

Offset: 0

Author

Bruno Berselli, Jun 09 2013

Keywords

• nonn
• easy

Comments

Sum of n-th hendecagonal number and n-th dodecagonal number.

Sum of reciprocals of a(n), for n > 0: 0.59314195720519963010713286193275...

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A051624, A051682, A051873.

Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=19: see list in A226488.

Programs

Magma

[n*(19*n-15)/2: n in [0..50]];

Magma

I:=[0,2,23]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..45]]; // Vincenzo Librandi, Aug 18 2013

Mathematica

Table[n (19 n - 15)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 17 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{3,-3,1},{0,2,23},50] (* Harvey P. Dale, Aug 17 2017 *)

PARI

a(n)=n*(19*n-15)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: x*(2+17*x)/(1-x)^3.

From Elmo R. Oliveira, Dec 27 2024: (Start)

E.g.f.: exp(x)*x*(4 + 19*x)/2.

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

a(n) = n + A051873(n). (End)