0,4

Row sums except n=0 are zero.

Example:p(x,3)=27 - 39 x + 13 x^2 - x^3;

M[3]={{9, 0, 0}, {3, 3, 0}, {-2, 1, 1}}.

Triangle T(n,k), 0<=k<=n, read by rows given by [1,q-1,q^2,q^3-q,q^4,q^5-q^2,q^6,q^7-q^3,q^8,...] DELTA [ -1,0,-q,0,-q^2,0,-q^3,0,-q^4,0,...](for q=3)=[1,2,9,24,81,234,729,2160,6561,...] DELTA [ -1,0,-3,0,-9,0,-27,0,-81,0,-243,0,...] where DELTA is the operator defined in A084938 ; see A122006 and A000244 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 09 2009]

q=3;

m(n,k)=If[k == m, q^(n - k), If[m == 1 && k < n, q^(n - k), If[k == n && m == 1, -(n-1), If[ k == n && m > 1, 1, 0]]]].

{1},

{1, -1},

{3, -4, 1},

{27, -39, 13, -1},

{729, -1080, 390, -40, 1},

{59049, -88209, 32670, -3630, 121, -1},

{14348907, -21493836, 8027019, -914760, 33033, -364, 1},

{10460353203, -15683355351, 5873190687, -674887059, 24995817, -298389, 1093, -1},

{22876792454961, -34309958505840, 12860351387820, -1481851188720, 55340738838, -677572560, 2688780, -3280, 1},

{150094635296999121, -225130514549271201, 84411075413992860, -9735286000579740, 364572438704838, -4500894304998, 18318658140, -24208860, 9841, -1},

{2954312706550833698643, -4431394012508602048404, 1661688327888170734581, -191704045424825015280, 7185614597027906094, -88955675043980472, 365067042474618, -494821649520, 217909263, -29524, 1}

Clear[f, q, M, n, m];

q = 3;

f[k_, m_] := If[k == m, q^(n - k), If[m == 1 && k < n, q^(n - k), If[k == n && m == 1, -(n-1), If[k == n && m > 1, 1, 0]]]];

M[n_] := Table[f[k, m], {k, 1, n}, {m, 1, n}];

Table[M[n], {n, 1, 10}];

Join[{1}, Table[Expand[CharacteristicPolynomial[M[n], x]], {n, 1, 7}]];

a = Join[{{ 1}}, Table[CoefficientList[CharacteristicPolynomial[M[n], x], x], {n, 1, 7}]];

Flatten[a]

A135950 , A022166

Sequence in context: A113084 A055325 A134049 this_sequence A123951 A123127 A077451

Adjacent sequences: A157780 A157781 A157782 this_sequence A157784 A157785 A157786

sign,tabl,uned

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 06 2009