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Search: id:A109086
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| A109086 |
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Recursively defined polynomials, read by row. |
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+0
5
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| 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 4, 2, 7, 4, 6, 2, 1, 1, 0, 8, 4, 30, 25, 72, 68, 116, 102, 118, 84, 67, 33, 16, 4, 1, 1, 0, 16, 8, 124, 114, 641, 776, 2495, 3372, 7637, 10444, 18561, 24212, 35684, 42828, 53707, 57884, 62257, 59056, 54261, 44356, 34326, 23548
(list; table; graph; listen)
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OFFSET
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1,8
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COMMENT
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lim(N->infinity)p_N(x)/prod(n = 0, N-1)p_n(x) = f(x), with f(x) from A109087.
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FORMULA
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p_0(x) = x, p_(n+1)(x) = p_n(x)^2 + prod(i = 0, n-1)p_i(x)^(n-i), n >= 0. p_n(x) = sum(i = 0, 2^n)t(n, i)*x^i, n >= 0. a(2^(n+1)+n-i)=t(n, i), n>=0, 0<=i<=2^n.
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EXAMPLE
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p_0(x) = x, p_1(x) = x^2 + 1, p_2(x) = x^4 + 2*x^2 + x + 1,
p_3(x) = x^8 + 4*x^6 + 2*x^5 + 7*x^4 + 4*x^3 + 6*x^2 + 2*x + 1
p_4(x) = x^16 + 8*x^14 + 4*x^13 + 30*x^12 + 25*x^11 + 72*x^10 + 68*x^9 + 116*x^8 + 102*x^7 + 118*x^6 + 84*x^5 + 67*x^4 + 33*x^3 + 16*x^2 + 4*x + 1
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PROGRAM
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(PARI) N=5; p=x; q=1; r=1; for(n=0, N, print(Vec(p)); q*=r; r*=p; p=p^2+q)
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CROSSREFS
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Cf. A109088, A109089, A109090.
Sequence in context: A111941 A153462 A126310 this_sequence A105794 A160380 A122433
Adjacent sequences: A109083 A109084 A109085 this_sequence A109087 A109088 A109089
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Nikolaus Meyberg (Nikolaus.Meyberg(AT)t-online.de), Jun 19 2005
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