A133335 a(3*n) = 3*a(3*n-1)-3*a(3*n-2)+2*a(3*n-3), a(3*n+1) = 3*a(3*n)-3*a(3*n-1)+2*a(3*n-2), a(3*n+2) = 3*a(3*n+1)-3*a(3*n) with a(0)=1, a(1)=2, a(2)=3.

1, 2, 3, 5, 10, 15, 25, 50, 75, 125, 250, 375, 625, 1250, 1875, 3125, 6250, 9375, 15625, 31250, 46875, 78125, 156250, 234375, 390625, 781250, 1171875, 1953125, 3906250, 5859375, 9765625, 19531250, 29296875, 48828125, 97656250, 146484375, 244140625, 488281250

Offset

0,2

Comments

a(0) = 1, a(1) = 2, for n >= 3: a(n-1) < a(n) = natural numbers such that (a(n-2)+a(n-1)+a(n))*a(n-1)/(a(n-2)*a(n)) are integers m > 1. Corresponding values of m for n>=3: 4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,3,3,4,... a(3*k) = a(3*k-1) + a(3*k-2), a(3*k+1) = 2*a(3*k), a(3*k+2) = a(3*k+1) + a(3*k) for k >= 1. [Jaroslav Krizek, Nov 26 2009]

Links

Table of n, a(n) for n=0..37.

D. Panario, M. Sahin, Q. Wang, A family of Fibonacci-like conditional sequences, INTEGERS, Vol. 13, 2013, #A78.

Index entries for linear recurrences with constant coefficients, signature (0,0,5).

Formula

a(n) = 5*a(n-3). G.f.: -(3*x^2+2*x+1)/(5*x^3-1). [Colin Barker, Oct 11 2012]

Mathematica

RecurrenceTable[{a[0]== 1, a[1]==2, a[2] == 3, a[n]== 5 a[n-3]}, a, {n, 40}] (* Vincenzo Librandi, Sep 11 2018 *)

Crossrefs

Sequence in context: A048329 A252659 A004691 * A062925 A118728 A062860

Adjacent sequences: A133332 A133333 A133334 * A133336 A133337 A133338

Keyword

nonn,easy

Author

Paul Curtz, Oct 19 2007

Extensions

More terms after a(14) by Jaroslav Krizek, Nov 26 2009

Status

approved