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Search: id:A052948
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| A052948 |
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Number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < 6 and |s(i) - s(i-1)| <= 1 for i = 1,2,....,n, s(0) = 3, s(n) = 3. |
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+0
5
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| 1, 1, 3, 7, 19, 51, 139, 379, 1035, 2827, 7723, 21099, 57643, 157483, 430251, 1175467, 3211435, 8773803, 23970475, 65488555, 178918059, 488813227, 1335462571, 3648551595, 9968028331, 27233159851, 74402376363, 203271072427
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In general a(n,m,j,k)=(2/m)*Sum(r,1,m-1,Sin(j*r*Pi/m)Sin(k*r*Pi/m)(1+2Cos(Pi*r/m))^n) is the number of (s(0), s(1), ..., s(n)) such that 0 < s(i) < m and |s(i) -s(i-1)| <= 1 for i = 1,2,....,n, s(0) = j, s(n) = k. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
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LINKS
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INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1007
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FORMULA
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G.f.: -(-1+2*x)/(1-3*x+2*x^3)
Recurrence: {a(1)=1, a(0)=1, -2*a(n)-2*a(n+1)+a(n+2)+1}
Sum(1/3*_alpha^(-n), _alpha=RootOf(1-3*_Z+2*_Z^3))
a(n)=1/3+(1+sqrt(3))^n/3+(1-sqrt(3))^n/3. Binomial transform of A025192 (with interpolated zeros). - Paul Barry (pbarry(AT)wit.ie), Sep 16 2003
a(n)=(1/3)*Sum(k, 1, 5, Sin(Pi*k/2)^2(1+2Cos(Pi*k/6))^n) - Herbert Kociemba (kociemba(AT)t-online.de), Jun 02 2004
a(0) = a(1) = 1; a(n+2) = 2*a(n+1) + 2*a(n) - 1 [From Carl R. White (oeisfan(AT)phodd.net), Jul 30 2009]
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MAPLE
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spec := [S, {S=Sequence(Prod(Union(Sequence(Prod(Sequence(Z), Z)), Z), Z))}, unlabeled ]: seq(combstruct[count ](spec, size=n), n=0..20);
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PROGRAM
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sage: from sage.combinat.sloane_functions import recur_gen2b sage: it = recur_gen2b(1, 1, 2, 2, lambda n: -1) sage: [it.next() for i in xrange(0, 29)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 09 2008
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CROSSREFS
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Cf. A026150 [From Carl R. White (oeisfan(AT)phodd.net), Jul 30 2009]
Sequence in context: A087224 A078059 A018031 this_sequence A026325 A002426 A011769
Adjacent sequences: A052945 A052946 A052947 this_sequence A052949 A052950 A052951
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KEYWORD
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easy,nonn
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000
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