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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 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 January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)