A051405 a(n) = (3^n+1)*(3^(n+1)+1)/4.

2, 10, 70, 574, 5002, 44530, 399310, 3589414, 32291602, 290585050, 2615147350, 23535971854, 211822683802, 1906400965570, 17157599124190, 154418363419894, 1389765184685602, 12507886403890090, 112570976860169830, 1013138789417005534

Offset

0,1

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (13, -39, 27).

Formula

a(0)=2, a(1)=10, a(2)=70, a(n)=13*a(n-1)-39*a(n-2)+27*a(n-3). - Harvey P. Dale, Jul 13 2012

G.f.: ( -2+16*x-18*x^2 ) / ( (x-1)*(3*x-1)*(9*x-1) ). - R. J. Mathar, Nov 07 2015

a(n) = 2*A051406(n). - R. J. Mathar, Nov 07 2015

Mathematica

Table[(3^n+1)(3^(n+1)+1)/4, {n, 0, 20}] (* or *) LinearRecurrence[{13, -39, 27}, {2, 10, 70}, 20] (* Harvey P. Dale, Jul 13 2012 *)

Crossrefs

Sequence in context: A354307 A217938 A333902 * A005568 A036075 A212914

Adjacent sequences: A051402 A051403 A051404 * A051406 A051407 A051408

Keyword

nonn,easy

Author

Colin Mallows

Status

approved