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%I #20 Aug 22 2015 03:00:52
%S 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,
%T 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,
%U 352,-48,2,1,1,1,1,1,1
%N Triangle read by rows: coefficients of polynomials W_n(x), highest degree terms first.
%H K. Dilcher, K. B. Stolarsky, <a href="http://dx.doi.org/10.1007/s11139-014-9620-5">Nonlinear recurrences related to Chebyshev polynomials</a>, The Ramanujan Journal, 2014, Online Oct. 2014, pp. 1-23.
%F 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
%e Triangle of coefficients begins:
%e 1,
%e 1, 1,
%e 2, 1, 1,
%e 4, 1, 1, 1,
%e 8, 1, 1, 1,
%e 16, -4, 1, 1, 1, 1,
%e 32, -16, 2, 1, 1, 1, 1,
%e 64, -48, 8, 1, 1, 1, 1, 1,
%e 128, -128, 32, 1, 1, 1, 1, 1,
%e 256, -320, 112 -8, 1, 1, 1, 1, 1, 1,
%e 512, -768, 352 -48, 2, 1, 1, 1, 1, 1, 1,
%e ...
%e The actual polynomials are:
%e 0 1
%e 1 x^2 + 1
%e 2 2x^4 + x^2 + 1
%e 3 4x^6 + x^4 + x^2 + 1
%e 4 8x^8 + x^4 + x^2 + 1
%e 5 16x^10 - 4x^8 + x^6 + x^4 + x^2 + 1
%e 6 32x^12 - 16x^10 + 2x^8 + x^6 + x^4 + x^2 + 1
%e 7 64x^14 - 48x^12 + 8x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e 8 128x^16 - 128x^14 + 32x^12 + x^8 + x^6 + x^4 + x^2 + 1
%e 9 256x^18 - 320x^16 + 112x^14 - 8x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e 10 512x^20 - 768x^18 + 352x^16 - 48x^14 + 2x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e ...
%o (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
%Y Cf. A257597.
%K sign,tabl
%O 0,4
%A _N. J. A. Sloane_, Jun 06 2015
%E One typo in data corrected by _Michel Marcus_, Aug 22 2015
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