Search: id:A030192
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%I A030192
%S A030192 1,6,30,144,684,3240,15336,72576,343440,1625184,7690464,36391680,
%T A030192 172207296,814893696,3856118400,18247348224,86347378944,
%U A030192 408600184320,1933516832256,9149499887616
%N A030192 Scaled Chebyshev U-polynomial evaluated at sqrt(6)/2.
%C A030192 Binomial transform of A001834. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2009]
%D A030192 A. F. Horadam, Special properties of the sequence W_n(a,b; p,q), Fib. 
               Quart., 5.5 (1967), 424-434. Case n->n+1, a=0,b=1; p=6, q=-6.
%D A030192 W. Lang, On polynomials related to powers of the generating function 
               of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eqs. (38) 
               and (45), lhs, m=6.
%H A030192 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A030192 a(n) = center term in M^n * [1 1 1], where M = the 3X3 matrix [1 1 1 
               / 1 4 1 / 1 1 1]. M^n * [1 1 1] = [A083881(n) a(n) A083881(n)]. E.g. 
               a(3) = 144 since M^3 * [1 1 1] = [54 144 54] = [A083881(3) a(3) A083881(3)]. 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 18 2004
%F A030192 a(n)=(sqrt(6))^n*U(n, sqrt(6)/2), g.f.: 1/(6*(x^2-x+1/6)), a(2*k+1)=6^(k+1)*A001353(k), 
               a(2*k)=6^k*A001834(k)
%F A030192 Preceded by 0, this is the binomial transform of A001353. Its E.g.f. 
               is then exp(3x)sinh(sqrt(3)x)/sqrt(3). - Paul Barry (pbarry(AT)wit.ie), 
               May 09 2003
%F A030192 a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*6^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 28 2008]
%F A030192 ((3+sqrt3)^n-(3-sqrt3)^n)/sqrt12 [From Al Hakanson (hawkuu(AT)gmail.com), 
               Dec 29 2008]
%o A030192 (Other) sage: [lucas_number1(n,6,6) for n in xrange(1, 21)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A030192 Cf. A083881.
%Y A030192 Sequence in context: A026749 A003279 A082134 this_sequence A026376 A026899 
               A135160
%Y A030192 Adjacent sequences: A030189 A030190 A030191 this_sequence A030193 A030194 
               A030195
%K A030192 nonn,new
%O A030192 0,2
%A A030192 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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