A014915 a(1)=1, a(n) = n*3^(n-1) + a(n-1).

1, 7, 34, 142, 547, 2005, 7108, 24604, 83653, 280483, 930022, 3055786, 9964519, 32285041, 104029576, 333612088, 1065406345, 3389929279, 10750918570, 33996147910, 107218620331, 337346390797, 1059110761804, 3318547053652, 10379285465677, 32408789311195

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..600

Dillan Agrawal, Selena Ge, Jate Greene, Tanya Khovanova, Dohun Kim, Rajarshi Mandal, Tanish Parida, Anirudh Pulugurtha, Gordon Redwine, Soham Samanta, and Albert Xu, Chip-Firing on Infinite k-ary Trees, arXiv:2501.06675 [math.CO], 2025. See p. 14.

A. V. Kitaev, Meromorphic Solution of the Degenerate Third Painlevé Equation Vanishing at the Origin, arXiv:1809.00122 [math.CA], 2018.

Index entries for linear recurrences with constant coefficients, signature (7,-15,9).

Formula

From Henry Bottomley, Dec 18 2000: (Start)

a(n) = ((2*n-1)*3^n + 1)/4;

a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3);

a(n) = 1 + 2*3 + 3*3^2 + .. + n*3^(n-1);

a(n) = a(n-1) + A027471(n+1). (End)

G.f.: x/((1-x)*(1-3*x)^2). - Colin Barker, Jul 28 2012

a(n) = f^n(n)/2 with f(x) = 3*x-1. - Glen Gilchrist, Apr 10 2019

E.g.f.: exp(x)*(1 + exp(2*x)*(6*x - 1))/4. - Stefano Spezia, May 14 2024

Mathematica

LinearRecurrence[{7, -15, 9}, {1, 7, 34}, 25] (* L. Edson Jeffery, May 08 2015 *)

Prog

(Magma) [((2*n - 1)*3^n + 1)/4: n in [1..30]]; // Vincenzo Librandi, Jun 09 2011

Crossrefs

Cf. A027471, A059045.

Cf. A027261, A064017, A079272.

Sequence in context: A122611 A326245 A219756 * A137747 A273722 A005023

Adjacent sequences: A014912 A014913 A014914 * A014916 A014917 A014918

Keyword

nonn,easy,changed

Author

Olivier Gérard

Status

approved