{"version":9,"randomSeed":"5608ed66675ba63f7c08f07be4086502","graph":{"viewport":{"xmin":-1.2499999999999982,"ymin":-1.2500000000000018,"xmax":1.2500000000000018,"ymax":1.2499999999999982}},"expressions":{"list":[{"type":"expression","id":"64","color":"#000000","latex":"x\\le x+1","fillOpacity":"1"},{"type":"text","id":"54","text":"https://oeis.org/A053120"},{"type":"expression","id":"1","color":"#c74440","latex":"C=\\left[1,0,1,-1,0,2,0,-3,0,4,1,0,-8,0,8,0,5,0,-20,0,16,-1,0,18,0,-48,0,32,0,-7,0,56,0,-112,0,64,1,0,-32,0,160,0,-256,0,128\\right]"},{"type":"expression","id":"56","color":"#388c46","latex":"N=7","slider":{"hardMin":true,"hardMax":true,"min":"0","step":"1"}},{"type":"expression","id":"60","color":"#c74440","latex":"P\\left(n,x\\right)=\\sum_{k=0}^{n}\\left(C\\left[K\\left(n,k\\right)\\right]x^{k}\\right)"},{"type":"expression","id":"38","color":"#2d70b3","latex":"\\left[P\\left(n,x\\right)\\operatorname{for}n=\\left[0...N\\right]\\right]\\left\\{-1\\le x\\le1\\right\\}","lines":true,"colorLatex":"H"},{"type":"expression","id":"55","color":"#2d70b3","latex":"H=\\left[\\operatorname{hsv}\\left(\\frac{360}{N+1}\\cdot n,1,1\\right)\\operatorname{for}n=\\left[0...N\\right]\\right]"},{"type":"expression","id":"39","color":"#388c46","latex":"K\\left(a,b\\right)=\\frac{a\\left(a+1\\right)}{2}+b+1","labelSize":"medium"},{"type":"text","id":"58","text":"relation to cosine"},{"type":"expression","id":"68","color":"#000000","latex":"W=\\operatorname{rgb}\\left(255,255,255\\right)"},{"type":"expression","id":"59","color":"#000000","latex":"\\left[P\\left(n,\\cos\\left(x\\right)\\right)\\operatorname{for}n=\\left[0...N\\right]\\right]","hidden":true,"labelSize":"medium","colorLatex":"W"},{"type":"expression","id":"69","color":"#c74440","latex":"\\left[\\cos\\left(nx\\right)\\operatorname{for}n=\\left[0...N\\right]\\right]","hidden":true,"lineStyle":"DOTTED"},{"type":"text","id":"66","text":"\"a beautiful plot\" from Michael Trott's 1999 \"Graphica 1\""},{"type":"expression","id":"61","color":"#c74440","latex":"r=\\left[n+P\\left(n,\\frac{\\theta}{\\pi}-1\\right)\\operatorname{for}n=\\left[0,2,...N\\right]\\right]","hidden":true,"polarDomain":{"min":"0","max":"2\\pi"},"colorLatex":"H"}]}}