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 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 (list; table; graph; refs; listen; history; text; internal format)
 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 G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened 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}] Flatten[%] (* A203991 *) TableForm[Table[c[n], {n, 1, 10}]] (* Second program *) Table[(n+1)*Min[n-k+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(n-k+1, k), ", "))) \\ G. C. Greubel, Jul 23 2019 (Magma) [(n+1)*Min(n-k+1, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Jul 23 2019 (Sage) [[(n+1)*min(n-k+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(n-k+1, k) ))); # G. C. Greubel, Jul 23 2019 CROSSREFS Cf. A203991, A202453. Sequence in context: A240209 A047079 A207624 * A238812 A227269 A156353 Adjacent sequences: A203987 A203988 A203989 * A203991 A203992 A203993 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jan 09 2012 STATUS approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)