Search: id:A030221
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%I A030221
%S A030221 1,6,29,139,666,3191,15289,73254,350981,1681651,8057274,38604719,
%T A030221 184966321,886226886,4246168109,20344613659,97476900186,
%U A030221 467039887271,2237722536169,10721572793574,51370141431701
%N A030221 Chebyshev even indexed U-polynomials evaluated at sqrt(7)/2.
%C A030221 a(n) = L(n,-5)*(-1)^n, where L is defined as in A108299; see also A004253 
               for L(n,+5). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 01 2005
%C A030221 General recurrence is a(n)=(a(1)-1)*a(n-1)-a(n-2), a(1)>=4, lim n->infinity 
               a(n)= x*(k*x+1)^n, k =(a(1)-3), x=(1+sqrt((a(1)+1)/(a(1)-3)))/2. 
               Examples in OEIS: a(1)=4 gives A002878, primes in it A121534. a(1)=5 
               gives A001834, primes in it A086386. a(1)=6 gives A030221, primes 
               in it not in OEIS {29,139,3191,...}. a(1)=7 gives A002315, primes 
               in it A088165. a(1)=8 gives A033890, primes in it not in OEIS (does 
               there exist any ?). a(1)=9 gives A057080, primes in it not in OEIS 
               {71,34649,16908641,...}. a(1)=10 gives A057081, primes in it not 
               in OEIS {389806471,192097408520951,...}. [From Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), 
               Sep 02 2008]
%C A030221 Inverse binomial transform of A030240. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 19 2009]
%D A030221 W. Lang, On polynomials related to powers of the generating function 
               of Catalan's numbers, Fib. Quart. 38,5 (2000) 408-419; Eq.(44), rhs, 
               m=6.
%D A030221 K. Dilcher and K. B. Stolarsky, A Pascal-type triangle characterizing 
               twin primes, Amer. Math. Monthly, 112 (2005), 673-681. (see page 
               678)
%H A030221 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A030221 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A030221 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A030221 a(n) = 5*a(n-1)-a(n-2), a(-1)=-1, a(0)=1; a(n)=U(2*n, sqrt(7)/2); g.f.: 
               (1+x)/(x^2-5*x+1); a(n)=A004254(n)+A004254(n+1)
%F A030221 a(n) ~ (1/2 + 1/6*sqrt(21))*(1/2*(5 + sqrt(21)))^n - Joe Keane (jgk(AT)jgk.org), 
               May 16 2002
%F A030221 Let q(n, x)=sum(i=0, n, x^(n-i)*binomial(2*n-i, i)); then (-1)^n*q(n, 
               -7)=a(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 10 2002
%o A030221 (Other) sage: [(lucas_number2(n,5,1)-lucas_number2(n-1,5,1))/3 for n 
               in xrange(1,22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Nov 10 2009]
%Y A030221 Cf. A004253, A004254.
%Y A030221 Sequence in context: A045445 A026884 A110311 this_sequence A009153 A012325 
               A125785
%Y A030221 Adjacent sequences: A030218 A030219 A030220 this_sequence A030222 A030223 
               A030224
%K A030221 nonn,new
%O A030221 0,2
%A A030221 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)

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