A131665 -id:A131665 - cp's OEIS frontend

A131292 a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), a(0)=a(1)=a(2)=1.

1, 1, 1, 2, 3, 5, 6, 9, 9, 12, 9, 9, 0, -9, -27, -54, -81, -135, -162, -243, -243, -324, -243, -243, 0, 243, 729, 1458, 2187, 3645, 4374, 6561, 6561, 8748, 6561, 6561, 0, -6561, -19683, -39366, -59049, -98415, -118098, -177147, -177147, -236196, -177147, -177147, 0, 177147, 531441, 1062882, 1594323

Offset: 0

Paul Curtz, Sep 29 2007

Sequence is identical to its third differences in absolute value.

Index entries for linear recurrences with constant coefficients, signature (0, 3, 0, -3).

Cf. A131665 (0, 0, 1, 3, 6, 11).

Cf. A057083 (bisection). - R. J. Mathar, Jul 17 2009

A131292 := proc(n) option remember ; if n <= 2 then 1; elif n mod 2 = 1 then 3*(A131292(n-1)-A131292(n-2))+2*A131292(n-3) ; else 3*(A131292(n-1)-A131292(n-2)) ; fi ; end: seq(A131292(n),n=0..80) ; # R. J. Mathar, Oct 18 2007

Join[{1, 1},LinearRecurrence[{0, 3, 0, -3},{1, 2, 3, 5},51]] (* Ray Chandler, Sep 23 2015 *)

G.f.: (2*x^3-x^2-x+1)*(1+x)^2/(1-3*x^2+3*x^4). - R. J. Mathar, Jul 17 2009

More terms from R. J. Mathar, Oct 18 2007

A138278 Sequence identical to its third differences in absolute values.

Original entry on oeis.org

1, 2, 4, 8, 16, 24, 40, 80, 120, 200, 400, 600, 1000, 2000, 3000, 5000, 10000, 15000, 25000, 50000, 75000, 125000, 250000, 375000, 625000, 1250000, 1875000, 3125000, 6250000, 9375000, 15625000, 31250000, 46875000, 78125000, 156250000, 234375000, 390625000

Offset: 0

Paul Curtz, May 06 2008

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

Cf. A131292, A131665, A132158, A132418, A132658.

Join[{1,2,4},LinearRecurrence[{0,0,5},{8,16,24},40]] (* Harvey P. Dale, Dec 08 2011 *)

From R. J. Mathar, Mar 23 2010: (Start)
a(n) = 5*a(n-3), n>5.
G.f.: (3*x^3+6*x^4+4*x^5+1+2*x+4*x^2)/(1-5*x^3). (End)
Sum_{n>=0} 1/a(n) = 391/192. - Amiram Eldar, Jan 14 2024

Edited by Charles R Greathouse IV, Mar 18 2010

More terms from Harvey P. Dale, Dec 08 2011

cp's OEIS Frontend

A131292 a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), a(0)=a(1)=a(2)=1.

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