%I A124030
%S A124030 1,1,1,0,2,1,0,3,4,1,3,14,19,8,1,48,173,204,89,16,1,1505,4866,5173,2082,
               381,
%T A124030 32,1,108780,325990,316978,113481,18926,1580,64,1,19072536,53887686,48428411,
%U A124030 15201276,2206536,164222,6469,128,1,8332293760,22465873081,18859204368,
               5176293234
%V A124030 1,1,-1,0,-2,1,0,-3,4,-1,3,-14,19,-8,1,48,-173,204,-89,16,-1,1505,-4866,
               5173,-2082,381,
%W A124030 -32,1,108780,-325990,316978,-113481,18926,-1580,64,-1,19072536,-53887686,
               48428411,
%X A124030 -15201276,2206536,-164222,6469,-128,1,8332293760,-22465873081,18859204368,
               -5176293234
%N A124030 Binomial centered tridigonal matrices as a triangular sequence: t(n,m.d)=If[n 
               + m - 1 == d, binomial[d - 1, n - 1], If[n + m == d, -1, If[n + m 
               - 2 == d, -1, 0]]].
%C A124030 These are pretty matrices in terms of symmetry. Matrices: 1 X 1 {{1}} 
               2 X 2 {{1, -1}, {-1, 1}} 3 X 3 {{1, -1, 0}, {-1, 2, -1}, {0, -1, 
               1}} 4 X 4 {{1, -1, 0, 0}, {-1, 3, -1, 0}, {0, -1, 3, -1}, {0, 0, 
               -1, 1}} 5 X 5 {{1, -1, 0, 0, 0}, {-1, 4, -1, 0, 0}, {0, -1, 6, -1, 
               0}, {0, 0, -1, 4, -1}, {0, 0, 0, -1, 1}} 6 X 6 {{1, -1, 0, 0, 0, 
               0}, {-1, 5, -1, 0, 0, 0}, {0, -1, 10, -1, 0, 0}, {0, 0, -1, 10, -1, 
               0}, {0, 0, 0, -1, 5, -1}, {0, 0, 0, 0, -1, 1}}
%F A124030 t(n,m.d)=If[n + m - 1 == d, binomial[d - 1, n - 1], If[n + m == d, -1, 
               If[n + m - 2 == d, -1, 0]]]
%e A124030 Triangular sequence:
%e A124030 {1},
%e A124030 {1, -1},
%e A124030 {0, 2, 1},
%e A124030 {0, 3, 2, -1},
%e A124030 {3, -4, -11, 2, 1},
%e A124030 {48, -13, -106, 21, 6, -1},
%e A124030 {-1505, 36, 2693, -58, -129, 2, 1},
%e A124030 {-108780, 5530, 171342, -8705, -5290, 268,20, -1}
%t A124030 An[d_] := Table[If[n + m - 1 == d, Binomial[d - 1, n - 1], If[n + m ==d, 
               -1, If[n + m - 2 == d, -1, 0]]], {n, 1, d}, {m, 1, d}]; Join[An[1], 
               Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 
               1, 20}]]; Flatten[%]
%Y A124030 Sequence in context: A128908 A155112 A101603 this_sequence A166040 A106378 
               A094301
%Y A124030 Adjacent sequences: A124027 A124028 A124029 this_sequence A124031 A124032 
               A124033
%K A124030 uned,probation,sign
%O A124030 1,5
%A A124030 Roger Bagula (rlbagulatftn(AT)yahoo.com), Nov 01 2006