%I A089817
%S A089817 1,6,30,145,696,3336,15985,76590,366966,1758241,8424240,40362960,
%T A089817 193390561,926589846,4439558670,21271203505,101916458856,488311090776,
%U A089817 2339638995025,11209883884350,53709780426726,257339018249281
%N A089817 a(n)=5a(n-1)-a(n-2)+1.
%D A089817 F. M. van Lamoen, Square wreaths around hexagons, Forum Geometricorum, 
               6 (2006) 311-325.
%H A089817 F. M. van Lamoen, <a href="http://forumgeom.fau.edu/FG2006volume6/FG200637index.html">
               Article in Forum Geometricorum</a>
%H A089817 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A089817 Partial sums of Chebyshev sequence S(n,5)=U(n,5/2)=A004254(n).
%F A089817 For n>0 a(n-1)= sum{i=1..n}sum{j=1..i}b(n) with b(n) as in A004253.
%F A089817 a(n)=(2/3-sqrt(21)/7)(5/2-sqrt(21)/2)^n+(sqrt(21)/7+2/3)(sqrt(21)/2+5/
               2)^n-1/3; a(n)=sum{k=0..n, S(k, 5)}=sum{k=0..n, U(k, 5/2)} Chebyshev 
               polynomials of 2nd kind, A049310
%F A089817 G.f.: 1/((1-x)*(1-5*x+x^2)) = 1/(1-6*x+6*x^2-x^3).
%F A089817 a(n)= 6*a(n-1)-6*a(n-2)+a(n-3), n>=2, a(-1):=0, a(0)=1, a(1)=6.
%F A089817 a(n)= sum(S(k, 5), k=0..n) with S(k, x)=U(k, x/2) Chebyshev's polynomials 
               of the second kind.
%F A089817 a(n)= (S(n+1, 5)-S(n, 5) -1)/3, n>=0.
%Y A089817 Cf. A061278, A053142.
%Y A089817 Partial sums of A004254. Cf. A101368.
%Y A089817 Sequence in context: A026899 A135160 A046945 this_sequence A006320 A079738 
               A127741
%Y A089817 Adjacent sequences: A089814 A089815 A089816 this_sequence A089818 A089819 
               A089820
%K A089817 easy,nonn
%O A089817 0,2
%A A089817 Paul Barry (pbarry(AT)wit.ie), Nov 14 2003
%E A089817 Chebyshev comments from W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Aug 31 2004