A169723 3^(n-1)*(2*3^(n-1)+3)+1.

6, 28, 190, 1540, 13366, 118828, 1065070, 9572500, 86113126, 774900028, 6973745950, 62762650660, 564860667286, 5083736439628, 45753599258830, 411782307236020, 3706040506843846, 33354363786753628, 300189271756259710, 2701703438832768580

Offset: 1

Author

Alice V. Kleeva (alice27353(AT)gmail.com), Jan 19 2010

Keywords

• nonn
• easy

Comments

A subsequence of the triangular numbers A000217.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Alice V. Kleeva, Grid for this sequence
• Alice V. Kleeva, Illustration of initial terms
• Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva
• Robert Munafo, Sequence A169720, and two others by Alice V. Kleeva [Cached copy, in pdf format, included with permission]
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Cf. A169720-A169727, A100702.

Programs

Magma

I:=[6,28,190]; [n le 3 select I[n] else 13*Self(n-1)-39*Self(n-2)+27*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Dec 03 2012

Mathematica

LinearRecurrence[{13, -39, 27}, {6, 28, 190}, 50]  (* or *) CoefficientList[Series[(-6 + 50 x - 60 x^2)/((x - 1) (3 x - 1) (9 x - 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Dec 03 2012 *)

Formula

G.f.: x*(-6+50*x-60*x^2)/((x-1)*(3*x-1)*(9*x-1)). - Vincenzo Librandi, Dec 03 2012

a(n) = 13*a(n-1)-39*a(n-2)+27*a(n-3). - Vincenzo Librandi, Dec 03 2012

a(n) = 2*9^(n-1)+3^n+1. - Bruno Berselli, Dec 05 2012