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A005059 (5^n - 3^n)/2. 16
0, 1, 8, 49, 272, 1441, 7448, 37969, 192032, 966721, 4853288, 24325489, 121804592, 609554401, 3049366328, 15251614609, 76272421952, 381405156481, 1907154922568, 9536162033329, 47681972428112, 238413348924961, 1192077204978008, 5960417405949649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Number of lines passing through 3 points of an n-dimensional grid of points of side 3. - David W. Wilson, c. 1999

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Princeton University Press, 2016, pp. 65-79. ISBN 978-0-691-16403-8

Index entries for linear recurrences with constant coefficients, signature (8,-15).

FORMULA

a(n) = 8*a(n-1)-15*a(n-2). - Paul Barry, Mar 03 2003

G.f.: x/((1-3*x)*(1-5*x)). - Paul Barry, Mar 03 2003

a(n) = sum( k=1..n, 2^(k-1)*3^(n-k)*binomial(n,k) ). - Zerinvary Lajos, Sep 24 2006

a(n) = (r^n-s^n)/(r-s) with r=5 and s=3. - Sture Sjöstedt, Oct 17 2012

a(n) = sum( k=0..n-1, 3^k*5^(n-k-1) ) for n>0, a(0)=0. - Bruno Berselli, Aug 07 2013

EXAMPLE

For the fifth formula: a(4) = 1*125 + 3*25 + 9*5 + 27*1 = 272. [Bruno Berselli, Aug 07 2013]

MAPLE

A005059:=n->(5^n-3^n)/2: seq(A005059(n), n=0..30); # Wesley Ivan Hurt, Nov 18 2014

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b-15*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011*)

LinearRecurrence[{8, -15}, {0, 1}, 50] (* Sture Sjöstedt, Oct 17 2012 *)

PROG

(Sage) [lucas_number1(n, 8, 15) for n in xrange(0, 21)] /* Zerinvary Lajos, Apr 23 2009 */

(MAGMA) [(5^n - 3^n)/2: n in [0..30] ]; // Vincenzo Librandi, Aug 19 2011

(PARI) a(n)=(5^n-3^n)/2 \\ Charles R Greathouse IV, Jun 11 2013

CROSSREFS

Cf. A081199 (binomial transform), A006516 (inverse binomial transform).

Sequence in context: A081901 A283686 A026389 * A026719 A026774 A089383

Adjacent sequences:  A005056 A005057 A005058 * A005060 A005061 A005062

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 28 02:14 EDT 2017. Contains 284182 sequences.