

A203990


Symmetric matrix based on f(i,j) = (i+j)*min(i,j), by antidiagonals.


4



2, 3, 3, 4, 8, 4, 5, 10, 10, 5, 6, 12, 18, 12, 6, 7, 14, 21, 21, 14, 7, 8, 16, 24, 32, 24, 16, 8, 9, 18, 27, 36, 36, 27, 18, 9, 10, 20, 30, 40, 50, 40, 30, 20, 10, 11, 22, 33, 44, 55, 55, 44, 33, 22, 11, 12, 24, 36, 48, 60, 72, 60, 48, 36, 24, 12, 13, 26, 39, 52, 65, 78, 78, 65, 52, 39, 26, 13
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OFFSET

1,1


COMMENTS

This sequence represents the matrix M given by f(i,j) = (i+j)*min{i,j} for i >= 1 and j >= 1.
See A203991 for characteristic polynomials of principal submatrices of M, with interlacing zeros.


LINKS



EXAMPLE

Northwest corner:
2, 3, 4, 5, 6, 7
3, 8, 10, 12, 14, 16
4, 10, 18, 21, 24, 27
5, 12, 21, 32, 36, 40


MATHEMATICA

(* First program *)
f[i_, j_] := (i + j) Min[i, j];
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}]] (* A203990 *)
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}]
TableForm[Table[c[n], {n, 1, 10}]]
(* Second program *)
Table[(n+1)*Min[nk+1, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Jul 23 2019 *)


PROG

(PARI) for(n=1, 15, for(k=1, n, print1((n+1)*min(nk+1, k), ", "))) \\ G. C. Greubel, Jul 23 2019
(Magma) [(n+1)*Min(nk+1, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 23 2019
(Sage) [[(n+1)*min(nk+1, k) for n in (1..n)] for n in (1..15)] # G. C. Greubel, Jul 23 2019
(GAP) Flat(List([1..15], n> List([1..n], k> (n+1)*Minimum(nk+1, k) ))); # G. C. Greubel, Jul 23 2019


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



