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 A155688 A symmetrical triangle of polynomial coefficients that are von Koch like: b=1/4; p(x, n) = If[Mod[n, 4] == 2, (b*x - n/2)*p(x, n - 1), If[ Mod[n, 4] == 3, (x/2 - b*n + 1/2)*p(x, n - 1), If[ Mod[n, 4] == 0, (-b*x - n/2 + b)*p(x, n - 1), (x/2 + b*n)*p(x, n - 1)]]]; q(x,n)=(p(x,n)+x^n*(p(1/x,n))/b^n. 0
 2, 3, 3, -2, -14, -2, 8, -17, -17, 8, -32, -9, 226, -9, -32, -148, -85, 737, 737, -85, -148, 1672, 404, -6199, -2842, -6199, 404, 1672, -8416, 1744, 36297, -12993, -12993, 36297, 1744, -8416, 126016, -15504, -532423, 54438, 202722, 54438 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Row sums are: {2, 6, -18, -18, 144, 1008, -11088, 33264, -532224, -5854464, 111234816,...}. Using the IFS definition of Hans Lauweier, I made a polynomial product set with Substirutions: x->x and y->n. The fractal modulo four is: a = Table[Expand[(1/ b^n)*CoefficientList[ExpandAll[p[x, n]], x] + Reverse[(1/b^n)* CoefficientList[ExpandAll[p[x, n]], x]]], {n, 0, 128}]; b0 = Table[If[m <= n, Mod[ a[[n]][[m]], 4], 0], {m, 1, Length[a]}, {n, 1, Length[a]}]; ListDensityPlot[b0, Mesh -> False, Frame -> False, AspectRatio -> Automatic, ColorFunction -> Hue] REFERENCES Hans Lauweier, Fractals,Endlessly Repeated Geometrical Figures,Princeton University Press, Ne Jersey,1991,pages 98-99 LINKS FORMULA b=1/4; p(x, n) = If[Mod[n, 4] == 2, (b*x - n/2)*p(x, n - 1), If[ Mod[n, 4] == 3, (x/2 - b*n + 1/2)*p(x, n - 1), If[ Mod[n, 4] == 0, (-b*x - n/2 + b)*p(x, n - 1), (x/2 + b*n)*p(x, n - 1)]]]; q(x,n)=(p(x,n)+x^n*(p(1/x,n))/b^n. EXAMPLE {2}, {3, 3}, {-2, -14, -2}, {8, -17, -17, 8}, {-32, -9, 226, -9, -32}, {-148, -85, 737, 737, -85, -148}, {1672, 404, -6199, -2842, -6199, 404, 1672}, {-8416, 1744, 36297, -12993, -12993, 36297, 1744, -8416}, {126016, -15504, -532423, 54438, 202722, 54438, -532423, -15504, 126016}, {1134032, 111936, -4799127, -523664, 1149591, 1149591, -523664, -4799127, 111936, 1134032}, {-22679968, -1098304, 95967468, 4727137, -20196266, -2205318, -20196266, 4727137, 95967468, -1098304, -22679968} MATHEMATICA Clear[p, x, n, b, a, b0]; b = 1/4; p[x, 0] = 1; p[x, 1] = x/2 + b; p[x_, n_] := p[x, n] = If[Mod[n, 4] == 2, (b*x - n/2)*p[x, n - 1], If[Mod[n, 4] == 3, (x/2 - b*n + 1/2)*p[x, n - 1], If[Mod[n, 4] == 0, (-b*x - n/2 + b)*p[x, n - 1], (x/2 + b*n)*p[x, n - 1]]]]; Table[Expand[(1/b^n)*CoefficientList[ ExpandAll[p[x, n]], x] + Reverse[(1/b^n)*CoefficientList[ExpandAll[ p[x, n]], x]]], {n, 0, 10}]; Flatten[%] CROSSREFS Sequence in context: A153479 A153489 A153310 * A215490 A153592 A153878 Adjacent sequences:  A155685 A155686 A155687 * A155689 A155690 A155691 KEYWORD sign,tabl,uned AUTHOR Roger L. Bagula, Jan 24 2009 STATUS approved

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)