Search: id:A107597
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%I A107597
%S A107597 1,1,2,4,8,17,38,87,205,493,1203,2969,7389,18504,46561,117596,297883,
%T A107597 756388,1924484,4904830,12519121,31995286,81864992,209681349,537562018,
%U A107597 1379332297,3542013533,9102191107,23406301490,60226845008,155059899921
%N A107597 Antidiagonal sums of triangle A107105: a(n) = Sum_{k=0..n} A107105(n-k,
               k), where A107105(n,k) = C(n,k)*(C(n,k) + 1)/2.
%C A107597 Limit a(n+1)/a(n) = (sqrt(5)+3)/2.
%F A107597 a(n) = (A051286(n) + A000045(n+1))/2, where A000045(n+1) = Fibonacci(n+1) 
               and A051286(n) = Whitney number of level n.
%F A107597 G.f.: (1/(1-x-x^2) +1/sqrt((1+x+x^2)* (1-3*x+x^2)))/2. - Michael Somos 
               Jul 27 2007
%o A107597 (PARI) a(n)=(sum(k=0,n,binomial(n-k,k)^2)+fibonacci(n+1))/2
%o A107597 (PARI) {a(n)= if(n<0, 0, polcoeff( (1/(1-x-x^2) +1/sqrt((1+x+x^2)* (1-3*x+x^2)+ 
               x*O(x^n)))/2, n))} /* Michael Somos Jul 27 2007 */
%Y A107597 Cf. A107105, A051286, A000045.
%Y A107597 Sequence in context: A006196 A089796 A112482 this_sequence A082499 A100131 
               A119685
%Y A107597 Adjacent sequences: A107594 A107595 A107596 this_sequence A107598 A107599 
               A107600
%K A107597 nonn
%O A107597 0,3
%A A107597 Paul D. Hanna (pauldhanna(AT)juno.com), May 22 2005

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