A116973 If n mod 2 = 0 then (3^(n+3)-19)/8 else (3^(n+3)-1)/8.

1, 10, 28, 91, 271, 820, 2458, 7381, 22141, 66430, 199288, 597871, 1793611, 5380840, 16142518, 48427561, 145282681, 435848050, 1307544148, 3922632451, 11767897351, 35303692060, 105911076178, 317733228541, 953199685621

Offset

0,2

Comments

Number of moves to solve Type 4 Zig-Zag puzzle.

References

Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.

Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13th International Puzzle Party, Amsterdam, Aug 20 1993.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Formula

a(n):=2*a(n-1)+3*a(n-2)+5, a(0)=1; a(1)=1. [From Zerinvary Lajos, Dec 14 2008]

a(n) = (3^(n+3) - 19^((n+1) mod 2)))/8. - Wesley Ivan Hurt, Nov 13 2013

Maple

f:=n->if n mod 2 = 0 then (3^(n+3)-19)/8 else (3^(n+3)-1)/8; fi;
a[0]:=1:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+5 od: seq(a[n], n=1..33); # Zerinvary Lajos, Dec 14 2008

Mathematica

f[n_]:=Module[{c=3^(n+3)}, If[EvenQ[n], (c-19)/8, (c-1)/8]]; Array[f, 30, 0] (* Harvey P. Dale, Oct 23 2012 *)

Crossrefs

Sequence in context: A251319 A126364 A076712 * A352180 A350990 A264579

Adjacent sequences: A116970 A116971 A116972 * A116974 A116975 A116976

Keyword

nonn

Author

N. J. A. Sloane, Apr 01 2006

Status

approved