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Search: id:A068156
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| A068156 |
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G.f.: (x+2)(x+1)/((x-1)(x-2))=Sum(n=0,inf,a(n)(x/2)^n). |
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+0
6
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| 1, 3, 9, 21, 45, 93, 189, 381, 765, 1533, 3069, 6141, 12285, 24573, 49149, 98301, 196605, 393213, 786429, 1572861, 3145725, 6291453, 12582909, 25165821, 50331645, 100663293, 201326589, 402653181, 805306365, 1610612733
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of moves to solve Hard Pagoda puzzle.
Partial sums of A058295. Binomial transform of (1,2,4,2,4,2,4 ....) - Paul Barry (pbarry(AT)wit.ie), Feb 28 2003
a(n)=a(n-1)+ 3*2^(n-1); a(1)=3. - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Apr 17 2008
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REFERENCES
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Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.
Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13-th International Puzzle Party, Amsterdam, Aug 20 1993.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
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FORMULA
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a(0)=1 a(n)=A060482(2n+1). n >0 a(n+1)=2a(n)+3.
G.f.: (1+2x^2)/((1-2x)(1-x)) - Paul Barry (pbarry(AT)wit.ie), Feb 28 2003
a(n)=3*2^n+0^n-3 - Paul Barry (pbarry(AT)wit.ie), Sep 04 2003
a(n) = A099257(A033484(n)+1) = 2*A033484(n) + 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 09 2004
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MATHEMATICA
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a=0; lst={1}; k=3; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 15 2008]
a=3; lst={1, a}; k=6; Do[a+=k; AppendTo[lst, a]; k+=k, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 16 2008]
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CROSSREFS
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Sequence in context: A084569 A110964 A107351 this_sequence A166452 A052101 A063830
Adjacent sequences: A068153 A068154 A068155 this_sequence A068157 A068158 A068159
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Mar 12 2002
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