Search: id:A052948
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%I A052948
%S A052948 1,1,3,7,19,51,139,379,1035,2827,7723,21099,57643,157483,430251,
%T A052948 1175467,3211435,8773803,23970475,65488555,178918059,488813227,
%U A052948 1335462571,3648551595,9968028331,27233159851,74402376363,203271072427
%N A052948 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.
%C A052948 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
%H A052948 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=1007">
               Encyclopedia of Combinatorial Structures 1007</a>
%F A052948 G.f.: -(-1+2*x)/(1-3*x+2*x^3)
%F A052948 Recurrence: {a(1)=1, a(0)=1, -2*a(n)-2*a(n+1)+a(n+2)+1}
%F A052948 Sum(1/3*_alpha^(-n), _alpha=RootOf(1-3*_Z+2*_Z^3))
%F A052948 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
%F A052948 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
%F A052948 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]
%p A052948 spec := [S,{S=Sequence(Prod(Union(Sequence(Prod(Sequence(Z),Z)),Z),Z))},
               unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%o A052948 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
%Y A052948 Cf. A026150 [From Carl R. White (oeisfan(AT)phodd.net), Jul 30 2009]
%Y A052948 Sequence in context: A087224 A078059 A018031 this_sequence A026325 A002426 
               A011769
%Y A052948 Adjacent sequences: A052945 A052946 A052947 this_sequence A052949 A052950 
               A052951
%K A052948 easy,nonn
%O A052948 0,3
%A A052948 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052948 More terms from James A. Sellers (sellersj(AT)math.psu.edu), Jun 06 2000

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