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A203996 Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals. 3
2, 3, 3, 4, 6, 4, 5, 8, 8, 5, 6, 10, 12, 10, 6, 7, 12, 15, 15, 12, 7, 8, 14, 18, 20, 18, 14, 8, 9, 16, 21, 24, 24, 21, 16, 9, 10, 18, 24, 28, 30, 28, 24, 18, 10, 11, 20, 27, 32, 35, 35, 32, 27, 20, 11, 12, 22, 30, 36, 40, 42, 40, 36, 30, 22, 12, 13, 24, 33, 40, 45, 48 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

A203996 represents the matrix M given by f(i,j)=min{i(j+1),j(i+1)} for i>=1 and j>=1.  See A203997 for characteristic polynomials of principal submatrices of M, with interlacing zeros.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

Northwest corner:

2...3....4....5....6....7

3...6....8....10...12...14

4...8....12...15...18...21

5...10...15...20...24...28

MATHEMATICA

f[i_, j_] := Min[i (j + 1), j (i + 1)];

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

TableForm[m[6]] (* 6x6 principal submatrix *)

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

{n, 1, 12}, {i, 1, n}]]   (* A203996 *)

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[%]      (* A203997 *)

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

CROSSREFS

Cf. A203995, A202453.

Sequence in context: A213938 A031501 A279417 * A059442 A225273 A014410

Adjacent sequences:  A203993 A203994 A203995 * A203997 A203998 A203999

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 09 2012

STATUS

approved

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Last modified November 18 01:20 EST 2018. Contains 317279 sequences. (Running on oeis4.)