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A204166 Symmetric matrix based on f(i,j)=ceiling[(i+j)/2], by antidiagonals. 3
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A204166 represents the matrix M given by f(i,j)=ceiling[(i+j)/2] for i>=1 and j>=1.  See A204167 for characteristic polynomials of principal submatrices of M, with interlacing zeros.  See A204016 for a guide to other choices of M.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

Northwest corner:

1 2 2 3 3 4 4 5

2 2 3 3 4 4 5 5

2 3 3 4 4 5 5 6

3 3 4 4 5 5 6 6

MATHEMATICA

f[i_, j_] := Ceiling[(i + j)/2];

m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]

TableForm[m[8]] (* 8x8 principal submatrix *)

Flatten[Table[f[i, n + 1 - i],

  {n, 1, 15}, {i, 1, n}]]  (* A204166 *)

p[n_] := CharacteristicPolynomial[m[n], x];

c[n_] := CoefficientList[p[n], x]

TableForm[Flatten[Table[p[n], {n, 1, 10}]]]

Table[c[n], {n, 1, 12}]

Flatten[%]                 (* A204167 *)

TableForm[Table[c[n], {n, 1, 10}]]

CROSSREFS

Cf. A204167, A204016, A202453.

Sequence in context: A132173 A023968 A284248 * A227581 A263846 A178786

Adjacent sequences:  A204163 A204164 A204165 * A204167 A204168 A204169

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified January 22 10:32 EST 2018. Contains 298042 sequences.