Search: id:A073370
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%I A073370
%S A073370 1,1,1,3,2,1,5,7,3,1,11,16,12,4,1,21,41,34,18,5,1,43,94,99,60,25,6,1,
%T A073370 85,219,261,195,95,33,7,1,171,492,678,576,340,140,42,8,1,341,1101,1692,
%U A073370 1644,1106,546,196,52,9,1
%N A073370 Convolution triangle of A001045(n+1) (generalized (1,2)-Fibonacci), n>
               =0.
%C A073370 The g.f. for the row polynomials P(n,x) := sum(a(n,m)*x^m,m=0..n) is 
               1/(1-(1+x+2*z)*z). See Shapiro et al. reference and comment under 
               A053121 for such convolution triangles.
%C A073370 The column sequences (without leading zeros) give: A001045(n+1), A073371-9 
               for m=0..9. Row sums give A002605.
%C A073370 Riordan array (1/(1-x-2x^2),x/(1-x-2x^2)). - Paul Barry (pbarry(AT)wit.ie), 
               Mar 15 2005
%H A073370 W. Lang, <a href="http://www-itp.physik.uni-karlsruhe.de/~wl/EISpub/A073370.text">
               First 10 rows</a>.
%F A073370 a(n, m)=sum(binomial(n-k, m)*binomial(n-m-k, k)*2^k, k=0..floor((n-m)/
               2)) if n>m, else 0.
%F A073370 a(n, m)=(1*(n-m+1)*a(n, m-1)+2*2*(n+m)*a(n-1, m-1))/((1^2+4*2)*m), n>
               =m>=1, a(n, 0)=A001045(n+1), n>=0, else 0.
%F A073370 a(n, m)= (p(m-1, n-m)*1*(n-m+1)*a(n-m+1)+q(m-1, n-m)*2*(n-m+2)*a(n-m))/
               (m!*9^m), n>=m>=1, with a(n)=a(n, m=0) := A001045(n+1), else 0; p(k, 
               n) := sum(A(k, l)*n^(k-l), l=0..k) and q(k, n) := sum(B(k, l)*n^(k-l), 
               l=0..k) with the number triangles A(k, m) := A073399(k, m) and B(k, 
               m) := A073400(k, m).
%F A073370 G.f. for column m (without leading zeros): 1/(1-(1+2*x)*x)^(m+1), m>=0.
%F A073370 Number triangle T(n, k) with T(n, 0)=A001045(n), T(1, 1)=1, T(n, k)=0 
               if k>n, T(n, k)=T(n-1, k-1)+2T(n-2, k)+T(n-1, k) otherwise. - Paul 
               Barry (pbarry(AT)wit.ie), Mar 15 2005
%e A073370 {1},{1,1},{3,2,1},... (lower triangular matrix n>=m>=0).
%Y A073370 Sequence in context: A138483 A065366 A092879 this_sequence A129675 A081277 
               A079628
%Y A073370 Adjacent sequences: A073367 A073368 A073369 this_sequence A073371 A073372 
               A073373
%K A073370 nonn,easy,tabl
%O A073370 0,4
%A A073370 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 
               2002

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