Search: id:A030191
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%I A030191
%S A030191 1,5,20,75,275,1000,3625,13125,47500,171875,621875,2250000,8140625,
%T A030191 29453125,106562500,385546875,1394921875,5046875000,18259765625,
%U A030191 66064453125,239023437500
%N A030191 Scaled Chebyshev U-polynomial evaluated at sqrt(5)/2.
%C A030191 Number of (s(0), s(1), ..., s(2n+4)) such that 0 < s(i) < 10 and |s(i) 
               - s(i-1)| = 1 for i = 1,2,....,2n+4, s(0) = 1, s(2n+4) = 5. - Herbert 
               Kociemba (kociemba(AT)t-online.de), Jun 14 2004
%C A030191 Binomial transform of A002878 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 04 2005
%D A030191 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=5, q=-5.
%D A030191 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=5.
%H A030191 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A030191 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A030191 a(n)=(sqrt(5))^n*U(n, sqrt(5)/2), g.f.: 1/(5*(x^2-x+1/5)), a(2*k+1)=5^(k+1)*F(2*k+2), 
               F(n) = Fibonacci (A000045), a(2*k)=5^k*L(2*k+1), L(n) = Lucas (A000032)
%F A030191 a(n-1)=sum(k=0, n, C(n, k)*F(2*k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jun 21 2003
%F A030191 a(n) = 5*a(n-1)-5*a(n-2). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Oct 23 2003
%F A030191 a(n-1)=((5/2+sqrt(5)/2)^n-(5/2-sqrt(5)/2)^n)/sqrt(5) is the 2nd binomial 
               transform of Fib(n), the first binomial transform of Fib(2n) and 
               its n-th term is the n-th term of the third binomial transform of 
               Fib(3n) divided by 2^n. - Paul Barry (pbarry(AT)wit.ie), Mar 23 2004
%F A030191 a(n)=Sum_{k, 0<=k<=n}5^k*A109466(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 28 2006
%F A030191 a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*5^k. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 28 2008]
%o A030191 (Other) sage: [lucas_number1(n,5,5) for n in xrange(1, 22)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A030191 Sequence in context: A022633 A092490 A094828 this_sequence A093131 A000344 
               A061278
%Y A030191 Adjacent sequences: A030188 A030189 A030190 this_sequence A030192 A030193 
               A030194
%K A030191 nonn
%O A030191 0,2
%A A030191 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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