# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a122160 Showing 1-1 of 1 %I A122160 #8 May 17 2019 02:34:54 %S A122160 1,0,-1,-1,-1,1,-1,2,1,-1,-2,7,-3,-2,1,-1,7,-13,5,2,-1,-1,12,-34,30, %T A122160 -6,-3,1,0,5,-30,60,-45,9,3,-1,1,1,-41,130,-155,78,-10,-4,1,1,-6,-3, %U A122160 87,-220,229,-106,14,4,-1,2,-19,45,54,-378,609,-455,160,-15,-5,1,1,-15,73,-123,-89,609,-889,615,-205,20,5,-1,1,-24,164,-460 %N A122160 Identity matrices minus Steinbach matrices as characteristic polynomials to give a triangular array I[n]-An[i,j]-> P[k,x] P[k,n]->T[n,m). %C A122160 Remember? 1/(1-x)=Sum[x^n,{n,0,Infinitity}] So to try with the Steinbach field: (I-A[i,j])^(-1)=Sun[A[i,j]^n,{n,0,Infinity}] It doesn't appear it should be finite? But I-A[i,j] is finite--> zero? {{1,0,0}, {{1,1,1}, {{0,-1,-1}, {0,1,0}, {1,1,0}, {-1,0,0}, {0,0,1}} - 1,0,0}}= { -1,0,1}} Matrices: {{0, -1}, {-1, 1}}, {{0, -1, -1}, {-1, 0, 0}, {-1, 0, 1}}, {{0, -1, -1, -1}, {-1, 0, -1, 0}, {-1, -1, 1, 0}, {-1, 0, 0, 1}}, {{0, -1, -1, -1, -1}, {-1, 0, -1, -1, 0}, {-1, -1, 0, 0, 0}, {-1, -1, 0, 1, 0}, {-1, 0, 0, 0, 1}} %H A122160 P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31. %F A122160 I[n]-An[i,j]-> P[k,x] P[k,n]->T[n,m) %e A122160 {1}, %e A122160 {0, -1}, %e A122160 {-1, -1, 1}, %e A122160 {-1, 2, 1, -1}, %e A122160 {-2, 7, -3, -2, 1}, %e A122160 {-1, 7, -13, 5, 2, -1}, %e A122160 {-1, 12, -34, 30, -6, -3, 1}, %e A122160 {0, 5, -30, 60, -45, 9,3, -1}, %e A122160 {1, 1, -41, 130, -155, 78, -10, -4, 1} %t A122160 An[d_] := Table[If[n + m - 1 > d, 0, 1], {n, 1, d}, {m, 1, d}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[IdentityMatrix[d] - An[d], x], x], {d, 1, 20}]]; Flatten[%] %Y A122160 Cf. A065941, A122767, A123218, A066170, A122610. %K A122160 uned,tabl,sign %O A122160 1,8 %A A122160 _Gary W. Adamson_ and _Roger L. Bagula_, Oct 17 2006 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE