A172241 a(n) = (1/18)*(8^n - (-1)^n - 9).

0, 3, 28, 227, 1820, 14563, 116508, 932067, 7456540, 59652323, 477218588, 3817748707, 30541989660, 244335917283, 1954687338268, 15637498706147, 125099989649180, 1000799917193443, 8006399337547548, 64051194700380387

Offset: 1

Author

Ralf Stephan, Nov 20 2010

Keywords

• nonn
• easy

Comments

It appears that a(n) = A153234(3*n-1). - Bruno Berselli, May 03 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (8, 1, -8).

Programs

Maple

A172241:=n->(8^n-(-1)^n-9)/18: seq(A172241(n), n=1..30); # Wesley Ivan Hurt, May 02 2017

Mathematica

LinearRecurrence[{8,1,-8},{0,3,28},30] (* Harvey P. Dale, Oct 29 2023 *)

PARI

a(n)=(8^n-(-1)^n-9)/18

Formula

G.f.: x^2*(3 + 4*x)/((1 - x)*(1 + x)*(1 - 8*x)). - Adapted to the offset by Bruno Berselli, May 03 2011

a(2*k) = 8*a(2*k-1) + 3 and a(2*k+1) = 8*a(2*k) + 4 for k>0, a(1)=0. - Yosu Yurramendi, Dec 30 2016