OFFSET
1,5
COMMENTS
Inspired by the Cornelius-Schultz article.
REFERENCES
Anthony Ralston and Philip Rabinowitz, A First Course in Numerical Analysis, 1978, ISBN 0070511586, see p. 256.
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows
E. F. Cornelius Jr. and P. Schultz, Sequences generated by polynomials, Amer. Math. Monthly, No. 2, 2008.
EXAMPLE
{1},
{1, -1},
{-1, -4, 1},
{-22, -7, 10, -1},
{-171, 148, 58, -20,1},
{97, 3238, -488, -237, 35, -1},
{45813, 30013, -28334, 631, 716, -56, 1},
{1235816, -772641, -587173, 160710, 2477, -1800, 84, -1}.
MATHEMATICA
a[n_] := n*(n + 1)/2; b[n_] = a[n] + 1;
T[n_, m_, d_] := If[ n == m, a[n], If[n == m - 1 || n == m + 1, If[n == m - 1, b[m - 1], If[ n == m + 1, b[n - 1], 0]], 0]]; M0[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; TableForm[Table[M0[n], {n, 1, 4}]];
p1 = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[M0[n + 1], x], x], {n, 0, 10}]]; (* sequence values *)
Flatten[p1] p[x, 0] = 1; p[x, -1] = 0; p[x_, j_] := p[x, j] = (x - a[j])*p[x, j - 1] - b[j - 1]^2*p[x, j - 2]; p2 = Join[{{1}}, Table[CoefficientList[(-1)^n*p[x, n], x], {n, 1, 11}]]; p1 - p2
CROSSREFS
KEYWORD
tabl,sign
AUTHOR
Roger L. Bagula, Feb 11 2008
EXTENSIONS
Edited by N. J. A. Sloane, Mar 02 2008
STATUS
approved