A226489 a(n) = n*(15*n-11)/2.

0, 2, 19, 51, 98, 160, 237, 329, 436, 558, 695, 847, 1014, 1196, 1393, 1605, 1832, 2074, 2331, 2603, 2890, 3192, 3509, 3841, 4188, 4550, 4927, 5319, 5726, 6148, 6585, 7037, 7504, 7986, 8483, 8995, 9522, 10064, 10621, 11193, 11780, 12382, 12999, 13631, 14278, 14940

Offset: 0

Author

Bruno Berselli, Jun 09 2013

Keywords

• nonn
• easy

Comments

Sum of n-th 9-gonal (nonagonal) number and n-th 10-gonal (decagonal) number.

Sum of reciprocals of a(n), for n > 0: 0.614629940137818703272919217222307...

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. A001106, A001107, A064761.

Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=15: see list in A226488.

Programs

Magma

[n*(15*n-11)/2: n in [0..50]];

Magma

I:=[0,2,19]; [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 (15 n - 11)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 13 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)

PARI

a(n)=n*(15*n-11)/2 \\ Charles R Greathouse IV, Oct 07 2015

Formula

G.f.: x*(2+13*x)/(1-x)^3.

a(n) + a(-n) = A064761(n).

From Elmo R. Oliveira, Jan 12 2025: (Start)

E.g.f.: exp(x)*x*(4 + 15*x)/2.

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