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 A133218 Indices of triangular numbers (A000217) that are also decagonal (A001107). 2
 0, 1, 4, 55, 154, 1885, 5248, 64051, 178294, 2175865, 6056764, 73915375, 205751698, 2510946901, 6989500984, 85298279275, 237437281774, 2897630548465, 8065878079348, 98434140368551, 274002417416074, 3343863141982285, 9308016314067184, 113592912687029155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Index entries for linear recurrences with constant coefficients, signature (1, 34, -34, -1, 1). FORMULA For n>5, a(n) = 34*a(n-2) - a(n-4) + 16. For n>6, a(n) = a(n-1) + 34*a(n-2) - 34*a(n-3) - a(n-4) + a(n-5). For n>1, a(n) = 1/8 * ((4 + sqrt(2)*(-1)^n)*(1+sqrt(2))^(2*n - 3) + (4 - sqrt(2)*(-1)^n)*(1-sqrt(2))^(2*n-3) - 4). a(n) = floor(1/8 * (4 + sqrt(2)*(-1)^n)* (1+sqrt(2))^(2*n-3)). G.f.: x^2*(2*x^4+3*x^3-17*x^2-3*x-1)/((x-1)*(x^2+6*x+1)*(x^2-6*x+1)). lim (n -> Infinity, a(2n+1)/a(2n)) = 1/7*(43 + 30*sqrt(2)). lim (n -> Infinity, a(2n)/a(2n-1)) = 1/7*(11 + 6*sqrt(2)). EXAMPLE The third number which is both triangular (A000217) and decagonal (A001107) is A133216(3)=10. Since this is the fourth triangular number, we have a(3) = 4. MATHEMATICA LinearRecurrence[{1, 34, -34, -1, 1 }, {0, 1, 4, 55, 154, 1885}, 24 ] CROSSREFS Cf. A000217, A001107, A133216, A133217. Sequence in context: A077658 A217124 A064439 * A190441 A151576 A204107 Adjacent sequences:  A133215 A133216 A133217 * A133219 A133220 A133221 KEYWORD nonn AUTHOR Richard Choulet, Oct 11 2007; Ant King, Nov 04 2011 EXTENSIONS Entry revised by Max Alekseyev, Nov 06 2011 STATUS approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)