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 A253822 Indices of centered triangular numbers (A005448) which are also octagonal numbers (A000567). 3
 1, 256, 833, 294848, 960705, 340253760, 1108652161, 392652543616, 1279383632513, 453120695078528, 1476407603267265, 522900889468077120, 1703773094786790721, 603427173325465917376, 1966152674976353224193, 696354435116698200574208, 2268938483149616833927425 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers y in the solutions to 6*x^2 - 3*y^2 - 4*x + 3*y - 2 = 0, the corresponding values of x being A253821. LINKS Colin Barker, Table of n, a(n) for n = 1..653 Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1). FORMULA a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5). G.f.: x*(255*x^3+577*x^2-255*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)). EXAMPLE 256 is in the sequence because the 256th centered triangular number is 97921, which is also the 181st octagonal number. MATHEMATICA LinearRecurrence[{1, 1154, -1154, -1, 1}, {1, 256, 833, 294848, 960705}, 20] (* Harvey P. Dale, Jul 19 2019 *) PROG (PARI) Vec(x*(255*x^3+577*x^2-255*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100)) CROSSREFS Cf. A000567, A005448, A253821, A253823. Sequence in context: A195091 A203450 A188248 * A258733 A209381 A236987 Adjacent sequences:  A253819 A253820 A253821 * A253823 A253824 A253825 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 14 2015 STATUS approved

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Last modified July 2 10:07 EDT 2022. Contains 355004 sequences. (Running on oeis4.)