The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A221564 The number of FO4C3 moves required to restore a packet of n playing cards to its original state (order and orientation), where each move Flips Over the top four (4) as a unit and then Cuts three (3) cards from the top to bottom. 1
 2, 4, 4, 4, 12, 12, 6, 24, 24, 8, 40, 40, 10, 60, 60, 12, 84, 84, 14, 112, 112, 16, 144, 144, 18, 180, 180, 20, 220, 220, 22, 264, 264, 24, 312, 312, 26, 364, 364, 28, 420, 420, 30, 480, 480, 32, 544, 544, 34, 612, 612, 36, 684, 684, 38, 760, 760, 40, 840, 840 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS Conjecture: a(3k+1) = 2k. The top card remains on top but is flipped over with each move. The remaining cards split into three cycles either of length 2*floor((n-1)/3) or 2*ceiling((n-1)/3). - Andrew Howroyd, Apr 27 2020 LINKS Andrew Howroyd, Table of n, a(n) for n = 4..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1). FORMULA a(3*n+1) = 2*n; a(3*n) = a(3*n-1) = 2*n*(n-1). - Andrew Howroyd, Apr 27 2020 From Colin Barker, Apr 29 2020: (Start) G.f.: 2*x^4*(1 + 2*x + 2*x^2 - x^3) / ((1 - x)^3*(1 + x + x^2)^3). a(n) = 3*a(n-3) - 3*a(n-6) + a(n-9) for n>12. (End) PROG (PARI) a(n)={2*((n-1)\3)*if(n%3==1, 1, (n-1)\3+1)} \\ Andrew Howroyd, Apr 27 2020 (PARI) Vec(2*x^4*(1 + 2*x + 2*x^2 - x^3) / ((1 - x)^3*(1 + x + x^2)^3) + O(x^40)) \\ Colin Barker, Apr 29 2020 CROSSREFS Cf. A225232. Sequence in context: A107058 A332336 A101449 * A134188 A140295 A291780 Adjacent sequences: A221561 A221562 A221563 * A221565 A221566 A221567 KEYWORD nonn,easy AUTHOR Colm Mulcahy, May 04 2013 EXTENSIONS a(16) corrected and terms a(17) and beyond from Andrew Howroyd, Apr 27 2020 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 8 21:25 EDT 2024. Contains 375759 sequences. (Running on oeis4.)