%I A053142
%S A053142 0,1,7,42,246,1435,8365,48756,284172,1656277,9653491,56264670,
%T A053142 327934530,1911342511,11140120537,64929380712,378436163736,
%U A053142 2205687601705,12855689446495,74928449077266,436715005017102
%N A053142 One half of A053141.
%H A053142 <a href="Sindx_Ch.html#Cheby">Index entries for sequences related to 
               Chebyshev polynomials.</a>
%F A053142 a(n)= (A001653(n)-1)/4.
%F A053142 a(n) := 6*a(n-1)-a(n-2)+1, a(0)=0, a(1)=1; G.f.: x/((1-x)*(1-6*x+x^2)).
%F A053142 a(n+1)=sum{k=0..n, S(k, 6)}=sum{k=0..n, U(n, 3)} Chebyshev polynomials 
               of 2nd kind, A049310; a(n+1)=(sqrt(2)-1)^(2n)(5/8-7sqrt(2)/16)+(sqrt(2)+1)^(2n)(7sqrt(2)/
               16 + 5/8)-1/4 - Paul Barry (pbarry(AT)wit.ie), Nov 14 2003
%F A053142 a(n) = 7a(n-1)-7a(n-2)+a(n-3); a(n) = -(1/4)+(1-sqrt(2))/(-8*sqrt(2))*(3-2*sqrt(2))^n+(1+sqrt(2))/
               (8*sqrt(2))*(3+2*sqrt(2))^n. - Antonio Alberto Olivares (tonioolivares(AT)todito.com), 
               Jan 13 2004
%F A053142 a(n)=sum{k=0..n, sum{j=0..2k, (-1)^(j+1)*Pell(j)*Pell(2k-j)}}, Pell(n)=A000129(n). 
               [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]
%Y A053142 Cf. A001653, A053141.
%Y A053142 Cf. A001653, A053141. Partial sums of A001109 - Barry Williams May 03 
               2000.
%Y A053142 Cf. A001652, A046090, A001653.
%Y A053142 Sequence in context: A030240 A054890 A102594 this_sequence A094168 A003949 
               A033133
%Y A053142 Adjacent sequences: A053139 A053140 A053141 this_sequence A053143 A053144 
               A053145
%K A053142 nonn,easy
%O A053142 0,3
%A A053142 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)