Search: id:A094706
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%I A094706
%S A094706 0,1,4,13,38,105,280,729,1866,4717,11812,29365,72590,178641,438064,
%T A094706 1071153,2613138,6362965,15470140,37565389,91125206,220864377,534951112,
%U A094706 1294960905,3133261530,7578261181,18323338324,44292046693,107041649438
%N A094706 Convolution of Pell(n) and 2^n.
%C A094706 a(n) = sum of n-th row in A101164 = A000129(n)-A000079(n). - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 03 2004
%F A094706 G.f. : x/((1-2x-x^2)(1-2x)); a(n)=sum{k=0..n, ((1+sqrt(2))^n-(1-sqrt(2))^n)/
               (2sqrt(2))2^(n-k)}; a(n)=(1+sqrt(2))^n(1+3sqrt(2)/4)+(1-sqrt(2))^n(1-3sqrt(2)/
               4)-2^(n+1); a(n)=4a(n-1)-3a(n-2)-2a(n-3).
%F A094706 a(n)=sum{k=0..floor(n/2), binomial(n-k, k+1)2^(n-2k-1)}; a(n)=sum{k=0..n, 
               binomial(k, n-k+1)2^k*(1/2)^(n-k+1)}. - Paul Barry (pbarry(AT)wit.ie), 
               Oct 07 2004
%Y A094706 Cf. A000129, A000079.
%Y A094706 Sequence in context: A089092 A049611 A084851 this_sequence A056014 A159036 
               A058693
%Y A094706 Adjacent sequences: A094703 A094704 A094705 this_sequence A094707 A094708 
               A094709
%K A094706 easy,nonn
%O A094706 0,3
%A A094706 Paul Barry (pbarry(AT)wit.ie), May 21 2004

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