# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a112739
Showing 1-1 of 1

%I A112739 #10 Feb 23 2014 12:39:14
%S A112739 1,1,1,1,2,1,1,3,2,1,1,4,5,2,1,1,5,10,7,2,1,1,6,17,22,9,2,1,1,7,26,53,
%T A112739 46,11,2,1,1,8,37,106,161,94,13,2,1,1,9,50,187,426,485,190,15,2,1,1,
%U A112739 10,65,302,937,1706,1457,382,17,2,1,1,11,82,457,1814,4687,6826,4373,766,19
%N A112739 Array counting nodes in rooted trees of height n in which the root and internal nodes have valency k (and the leaf nodes have valency one).
%C A112739 Rows of the square array have g.f. (1+x)/((1-x)(1-kx)). They are the partial sums of the coordination sequences for the infinite tree of valency k. Row sums are A112740.
%C A112739 Rows of the square array are successively: A000012, A040000, A005408, A033484, A048473, A020989, A057651, A061801, A238275, A238276, A138894, A090843, A199023. - _Philippe Deléham_, Feb 22 2014
%D A112739 L. He, X. Liu and G. Strang, (2003) Trees with Cantor Eigenvalue Distribution. Studies in Applied Mathematics 110 (2), 123-138.
%D A112739 L. He, X. Liu and G. Strang, Laplacian eigenvalues of growing trees, Proc. Conf. on Math. Theory of Networks and Systems, Perpignan (2000).
%F A112739 As a square array read by antidiagonals, T(n, k)=sum{j=0..k, (2-0^j)*(n-1)^(k-j)}; T(n, k)=(n(n-1)^k-2)/(n-2), n<>2, T(2, n)=2n+1; T(n, k)=sum{j=0..k, (n(n-1)^j-0^j)/(n-1)}, j<>1. As a triangle read by rows, T(n, k)=if(k<=n, sum{j=0..k, (2-0^j)*(n-k-1)^(k-j)}, 0).
%e A112739 As a square array, rows begin
%e A112739 1,1,1,1,1,1,... (A000012)
%e A112739 1,2,2,2,2,2,... (A040000)
%e A112739 1,3,5,7,9,11,... (A005408)
%e A112739 1,4,10,22,46,94,... (A033484)
%e A112739 1,5,17,53,161,485,... (A048473)
%e A112739 1,6,26,106,426,1706,... (A020989)
%e A112739 1,7,37,187,937,4687,... (A057651)
%e A112739 1,8,50,302,1814,10886,... (A061801)
%e A112739 As a number triangle, rows start
%e A112739 1;
%e A112739 1,1;
%e A112739 1,2,1;
%e A112739 1,3,2,1;
%e A112739 1,4,5,2,1;
%e A112739 1,5,10,7,2,1;
%Y A112739 Cf. A112468, A000012, A040000, A005408, A033484, A048473, A020989, A057651, A061801, A238275, A238276, A138894, A090843, A199023.
%K A112739 easy,nonn,tabl
%O A112739 0,5
%A A112739 _Paul Barry_, Sep 16 2005

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE