A257597 Irregular triangle read by rows: coefficients of polynomials V_n(x), highest degree terms first.

1, 1, -1, 1, -3, 1, -7, 1, 1, -15, 5, 1, -31, 17, -1, 1, -63, 49, -7, 1, -127, 129, -31, 1, 1, -255, 321, -111, 9, 1, -511, 769, -351, 49, -1, 1, -1023, 1793, -1023, 209, -11, 1, -2047, 4097, -2815, 769, -71, 1, 1, -4095, 9217, -7423, 2561, -351, 13, 1, -8191, 20481, -18943, 7937, -1471, 97, -1

Offset

1,5

Links

Table of n, a(n) for n=1..63.

K. Dilcher, K. B. Stolarsky, Nonlinear recurrences related to Chebyshev polynomials, The Ramanujan Journal, 2014, Online Oct. 2014, pp. 1-23.

Example

Triangle begins:
1,
1, -1,
1, -3,
1, -7, 1,
1, -15, 5,
1, -31, 17, -1,
1, -63, 49, -7,
1, -127, 129, -31, 1,
1, -255, 321, -111, 9,
1, -511, 769, -351, 49, -1,
1, -1023, 1793, -1023, 209, -11,
1, -2047, 4097, -2815, 769, -71, 1,
1, -4095, 9217, -7423, 2561, -351, 13,
1, -8191, 20481, -18943, 7937, -1471, 97, -1,
...

Prog

(PARI) tabf(nn) = {pp = 1; p = x; print(polcoeff(p, poldegree(p))); for (n=1, nn, np = 2*x*p-pp-x^(n+1); forstep (j=poldegree(np), 0, -1, if (c = polcoeff(np, j), print1(c, ", ")); ); pp = p; p = np; print(); ); } \\ Michel Marcus, Aug 22 2015

Crossrefs

A210197 is an essentially identical triangle.

Sequence in context: A242114 A143470 A114580 * A097229 A097862 A097612

Adjacent sequences: A257594 A257595 A257596 * A257598 A257599 A257600

Keyword

sign,tabf

Author

N. J. A. Sloane, Jun 06 2015

Status

approved