%I #2 Mar 30 2012 17:25:32
%S 1,4,1,7,4,5,10,7,20,16,13,10,35,64,53,16,13,50,112,212,175,19,16,65,
%T 160,371,700,578,22,19,80,208,530,1225,2312,1909,25,28,95,256,689,
%U 1750,4046,7636,6305,28,25,110,304,848,2275,5780,23363,25220,20824
%N Eigentriangle by rows, A143971 * (A108300 * 0^(n-k)); 1<=k<=1
%C Right border = A108300: (1, 1, 5, 16, 53, 175, 578,...). Row sums = (1, 5, 16, 53, 175, 578,...) = INVERT transform of (1, 4, 7, 10,...).
%C Sum of n-th row terms = rightmost term of next row.
%C Comment in A108300 states that (5, 16, 53, 175,...) is related to the numbers of hydrogen bonds in hydrocarbons.
%F Eigentriangle by rows, A143971 * (A108300 * 0^(n-k)); 1<=k<=1
%F Triangle A143971 = (1; 4,1; 7,4,1; 10,7,4,1;...). A108300 * 0^(n-k) = an infinite lower triangular matrix with A108300 (1, 1, 5, 16, 53, 175, 578, 1909,...) in the main diagonal and the rest zeros. By rows, = termwise products of n-th row terms of A143971 and n terms of A108300.
%e First few rows of the triangle =
%e 1;
%e 4, 1;
%e 7, 4, 5;
%e 10, 7, 10, 16;
%e 13, 10, 35, 64, 53;
%e 16, 13, 50, 112, 212, 175;
%e 19, 16, 65, 160, 371, 700, 578;
%e 22, 19, 80, 208, 530, 1225, 2312, 1909;
%e 25, 22, 95, 256, 689, 1750, 4046, 7636, 6305;
%e ... Example: row 4 = (10, 7, 20, 16) = termwise products of (10, 7, 4, 1) and (1, 1, 5, 16) = (10*1, 7*1, 4*5, 1*16), where (10, 7, 4, 1) = row 4 of triangle A143971.
%Y A143971, Cf. A016777, A108300
%K nonn,tabl
%O 1,2
%A _Gary W. Adamson_, Sep 06 2008