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 A230081 Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power. 4
 0, 4, 13, 50, 173, 613, 2149, 7557, 26543, 93264, 327657, 1151183, 4044478, 14209634, 49923211, 175397097, 616229093, 2165020570, 7606447024, 26724012524, 93890464368, 329868851103, 1158940469863, 4071748539926, 14305425173111 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The formula for the nonpositive powers of rho(11) := 2*cos(Pi/11) (the length ratio (smallest diagonal/side) in the regular 11-gon), when written in the power basis of the degree 5 algebraic number field Q(rho(11)) is: 1/rho(11)^n = A038342(n)*1 + A230080*rho(11) - a(n)*rho(11)^2 - A069006(n-1)*rho(11)^3 + A038342(n-1)*rho(11)^4, n >= 0, with A069006(-1) = 0 = A038342(-1). LINKS Table of n, a(n) for n=0..24. Index entries for linear recurrences with constant coefficients, signature (3,3,-4,-1,1). FORMULA G.f.: x*(4 + x - x^2) / (1 - 3*x - 3*x^2 + 4*x^3 + x^4 - x^5). a(n) = 3*a(n-1) +3*a(n-2) -4*a(n-3) -a(n-4) +a(n-5) for n >= 0, with a(-5)=3, a(-4)=0, a(-3)=0, a(-2)=-1, a(-1)=0. EXAMPLE 1/rho(11)^4 = 146*1 + 73*rho(11) - 173*rho(11)^2 - 29*rho(11)^3 + 41*rho(11)^4 (approximately 0.07374164519). CROSSREFS Cf. A038342, A069006, A230080. Sequence in context: A149454 A101125 A284336 * A299699 A056275 A149455 Adjacent sequences: A230078 A230079 A230080 * A230082 A230083 A230084 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Nov 04 2013 STATUS approved

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Last modified June 2 20:13 EDT 2023. Contains 363100 sequences. (Running on oeis4.)