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 A205184 Period 12: repeat (1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9). 0
 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9, 1, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The terms of this sequence are the digital roots of the indices of those nonzero triangular numbers that are also perfect squares (A001108). LINKS Table of n, a(n) for n=1..86. Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 0, -1, 0, 1). FORMULA G.f.: x*(1+8*x+3*x^2+x^3+3*x^4-x^5+x^6+9*x^7) / ((1-x)*(1+x)*(1+x^2)*(1-sqrt(3)*x+x^2)*(1+sqrt(3)*x+x^2)). a(n) = a(n-12). a(n) = 25-a(n-1)-a(n-6)-a(n-7). a(n) = a(n-2)-a(n-6)+a(n-8). a(n) = 1/4*(25+(-1)^n*(9+4*sqrt(3)*(cos(n*Pi/6)-cos(5*n*Pi/6))+2*cos(n*Pi/2))). EXAMPLE As the fourth nonzero triangular number that is also a perfect square is A000217(288), and 288 has digital root A010888(288)=9, then a(4)=9. MATHEMATICA LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9}, 86] LinearRecurrence[{0, 1, 0, 0, 0, -1, 0, 1}, {1, 8, 4, 9, 7, 8, 7, 9}, 86] (* Ray Chandler, Aug 03 2015 *) PROG (PARI) a(n)=[9, 1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1][n%12+1] \\ Charles R Greathouse IV, Jul 17 2016 CROSSREFS Cf. A001108, A000217, A010888, A000290. Sequence in context: A338574 A011225 A011196 * A105144 A277781 A254767 Adjacent sequences: A205181 A205182 A205183 * A205185 A205186 A205187 KEYWORD nonn,easy AUTHOR Ant King, Jan 23 2012 STATUS approved

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Last modified September 29 23:48 EDT 2023. Contains 365781 sequences. (Running on oeis4.)