cp's OEIS Frontend

A080245 Inverse of coordination sequence array A113413.

%I A080245 #15 Feb 28 2023 17:04:21
%S A080245 1,-2,1,6,-4,1,-22,16,-6,1,90,-68,30,-8,1,-394,304,-146,48,-10,1,1806,
%T A080245 -1412,714,-264,70,-12,1,-8558,6752,-3534,1408,-430,96,-14,1,41586,
%U A080245 -33028,17718,-7432,2490,-652,126,-16,1
%N A080245 Inverse of coordination sequence array A113413.
%C A080245 Formal inverse of A035607 when written as lower triangular matrix 1 2 1 2 4 1 ...
%H A080245 Huyile Liang, Yanni Pei, and Yi Wang, <a href="https://arxiv.org/abs/2302.11856">Analytic combinatorics of coordination numbers of cubic lattices</a>, arXiv:2302.11856 [math.CO], 2023. See p. 7.
%F A080245 Essentially the same as the triangle T(n, k), for n>0 and k>0, given by [0, -2, -1, -2, -1, -2, -1, -2, ...] DELTA A000007. Triangle (unsigned) given by [0, 2, 1, 2, 1, 2, 1, 2, ...] DELTA A000007, where DELTA is Deléham's operator defined in A084938.
%F A080245 Riordan array ((sqrt(1+6x+x^2)-x-1)/(2x), (sqrt(1+6x+x^2)-x-1)/2).
%e A080245 Rows are {1}, {-2, 1}, {6, -4, 1}, {-22, 16, -6, 1}, ....
%e A080245 From _Paul Barry_, Apr 28 2009: (Start)
%e A080245 Triangle begins
%e A080245   1,
%e A080245   -2, 1,
%e A080245   6, -4, 1,
%e A080245   -22, 16, -6, 1,
%e A080245   90, -68, 30, -8, 1,
%e A080245   -394, 304, -146, 48, -10, 1,
%e A080245   1806, -1412, 714, -264, 70, -12, 1
%e A080245 Production matrix is
%e A080245   -2, 1,
%e A080245   2, -2, 1,
%e A080245   -2, 2, -2, 1,
%e A080245   2, -2, 2, -2, 1,
%e A080245   -2, 2, -2, 2, -2, 1,
%e A080245   2, -2, 2, -2, 2, -2, 1,
%e A080245   -2, 2, -2, 2, -2, 2, -2, 1 (End)
%Y A080245 Row sums are signed little Schroeder numbers A080243. Diagonal sums are given by A080244.
%Y A080245 Cf. A035607, A080243, A080244, A006603, A001003.
%Y A080245 Cf. A000007 A084938.
%Y A080245 Essentially same triangle as A033877 but with rows read in reversed order.
%K A080245 sign,tabl
%O A080245 0,2
%A A080245 _Paul Barry_, Feb 13 2003