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

1,1

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A169720-A169727, A100702.

Sequence in context: A278015 A338810 A345002 * A052395 A034660 A347770

Adjacent sequences: A169720 A169721 A169722 * A169724 A169725 A169726

Keyword

nonn,easy

Author

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

Status

approved