A226491 a(n) = n*(21*n-17)/2.

0, 2, 25, 69, 134, 220, 327, 455, 604, 774, 965, 1177, 1410, 1664, 1939, 2235, 2552, 2890, 3249, 3629, 4030, 4452, 4895, 5359, 5844, 6350, 6877, 7425, 7994, 8584, 9195, 9827, 10480, 11154, 11849, 12565, 13302, 14060, 14839, 15639, 16460, 17302, 18165, 19049, 19954

Offset: 0

Author

Bruno Berselli, Jun 09 2013

Keywords

• nonn
• easy

Comments

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

Sum of reciprocals of a(n), for n > 0: 0.58517199913243139233033474262449...

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, A051865, A064762.

Cf. numbers of the form n*(n*k - k + 4)/2, this sequence is the case k=21: see list in A226488.

Programs

Magma

[n*(21*n-17)/2: n in [0..50]];

Magma

I:=[0,2,25]; [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 (21 n - 17)/2, {n, 0, 50}]
CoefficientList[Series[x (2 + 19 x) / (1 - x)^3, {x, 0, 45}], x] (* Vincenzo Librandi, Aug 18 2013 *)
LinearRecurrence[{3,-3,1},{0,2,25},50] (* Harvey P. Dale, Feb 01 2023 *)

PARI

a(n)=n*(21*n-17)/2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: x*(2+19*x)/(1-x)^3.

a(n) + a(-n) = A064762(n).

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

E.g.f.: exp(x)*x*(4 + 21*x)/2.

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