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A257598 Triangle read by rows: coefficients of polynomials W_n(x), highest degree terms first. 0
1, 1, 1, 2, 1, 1, 4, 1, 1, 1, 8, 1, 1, 1, 16, -4, 1, 1, 1, 1, 32, -16, 2, 1, 1, 1, 1, 64, -48, 8, 1, 1, 1, 1, 1, 128, -128, 32, 1, 1, 1, 1, 1, 256, -320, 112, -8, 1, 1, 1, 1, 1, 1, 512, -768, 352, -48, 2, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..63.

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

FORMULA

W(n) = V(n+1)^2 - V(n)*V(n+2) where V(n) are the polynomials defined in A257597. - Michel Marcus, Aug 22 2015

EXAMPLE

Triangle of coefficients begins:

1,

1, 1,

2, 1, 1,

4, 1, 1, 1,

8, 1, 1, 1,

16, -4, 1, 1, 1, 1,

32, -16, 2, 1, 1, 1, 1,

64, -48, 8, 1, 1, 1, 1, 1,

128, -128, 32, 1, 1, 1, 1, 1,

256, -320, 112 -8, 1, 1, 1, 1, 1, 1,

512, -768, 352 -48, 2, 1, 1, 1, 1, 1, 1,

...

The actual polynomials are:

0 1

1 x^2 + 1

2 2x^4 + x^2 + 1

3 4x^6 + x^4 + x^2 + 1

4 8x^8 + x^4 + x^2 + 1

5 16x^10 - 4x^8 + x^6 + x^4 + x^2 + 1

6 32x^12 - 16x^10 + 2x^8 + x^6 + x^4 + x^2 + 1

7 64x^14 - 48x^12 + 8x^10 + x^8 + x^6 + x^4 + x^2 + 1

8 128x^16 - 128x^14 + 32x^12 + x^8 + x^6 + x^4 + x^2 + 1

9 256x^18 - 320x^16 + 112x^14 - 8x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1

10 512x^20 - 768x^18 + 352x^16 - 48x^14 + 2x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1

...

PROG

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

CROSSREFS

Cf. A257597.

Sequence in context: A144383 A205553 A178411 * A294580 A294587 A064645

Adjacent sequences:  A257595 A257596 A257597 * A257599 A257600 A257601

KEYWORD

sign,tabl

AUTHOR

N. J. A. Sloane, Jun 06 2015

EXTENSIONS

One typo in data corrected by Michel Marcus, Aug 22 2015

STATUS

approved

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Last modified October 19 02:23 EDT 2018. Contains 316327 sequences. (Running on oeis4.)