Search: id:A033504
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%I A033504
%S A033504 1,10,66,372,1930,9516,45332,210664,960858,4319100,19188796,84438360,
%T A033504 368603716,1598231992,6889682280,29551095248,126193235194,536799072924,
%U A033504 2275560109868,9616650989560,40527780684972,170368957887656
%N A033504 a(n)/4^n is expected number of tosses of a coin required to obtain n 
               heads or n tails.
%C A033504 The number of rooted two-vertex n-edge maps in the plane (planar with 
               a distinguished outside face). - Valery A. Liskovets (liskov(AT)im.bas-net.by), 
               Mar 17 2005
%D A033504 M. Klamkin, ed., Problems in Applied Mathematics: Selections from SIAM 
               Review, SIAM, 1990; see pp. 127-129.
%D A033504 V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the 
               plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
%H A033504 V. A. Liskovets and T. R. Walsh, <a href="http://dx.doi:10.1016/j.aam.2005.03.006">
               Counting unrooted maps on the plane</a>, Advances in Applied Math., 
               36, No.4 (2006), 364-387.
%F A033504 With a different offset: Sum_{j=0..n} Sum_{k=0..n} binomial(n, j)*binomial(n, 
               k)*min(j, k) = n*2^(n-1) + (n/2)*binomial(2*n, n) [see Klamkin]
%F A033504 a(n-1) = b(n, n), where b(n, m) = b(n-1, m)/2+b(n, m-1)/2+1; b(n, 0)=b(0, 
               n)=0
%F A033504 a(n) = sum 2^(2 n - k - l) Binomial(k+l, k), where the sum is from 0 
               to n for k and l
%F A033504 a(n) = (2n+1)*sum_{0<=i, j<=n}binomial(2n, i+j)/(i+j+1) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Mar 05 2005
%F A033504 a(n) = (n+1)*(2^(2*n+1)-binomial(2*n+1,n+1)). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 23 2007
%Y A033504 Cf. A002457, A100511, A103943.
%Y A033504 Cf. A000346, A130783.
%Y A033504 Sequence in context: A080421 A004310 A026853 this_sequence A163615 A117305 
               A108275
%Y A033504 Adjacent sequences: A033501 A033502 A033503 this_sequence A033505 A033506 
               A033507
%K A033504 easy,nonn,nice
%O A033504 0,2
%A A033504 Michael Ulm (ulm(AT)mathematik.uni-ulm.de)

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