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 A253879 Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217). 3
 1, 9, 136, 2160, 34417, 548505, 8741656, 139317984, 2220346081, 35386219305, 563959162792, 8987960385360, 143243407002961, 2282906551662009, 36383261419589176, 579849276161764800, 9241205157168647617, 147279433238536597065, 2347229726659416905416 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Also positive integers y in the solutions to x^2 - 7*y^2 + x + 7*y - 2 = 0, the corresponding values of x being A253878. LINKS Colin Barker, Table of n, a(n) for n = 1..832 Index entries for linear recurrences with constant coefficients, signature (17,-17,1). FORMULA a(n) = 17*a(n-1)-17*a(n-2)+a(n-3). G.f.: x*(8*x-1) / ((x-1)*(x^2-16*x+1)). a(n) = (14-(8-3*sqrt(7))^n*(7+3*sqrt(7))+(-7+3*sqrt(7))*(8+3*sqrt(7))^n)/28. - Colin Barker, Mar 04 2016 EXAMPLE 9 is in the sequence because the 9th centered heptagonal number is 253, which is also the 22nd triangular number. PROG (PARI) Vec(x*(8*x-1)/((x-1)*(x^2-16*x+1)) + O(x^100)) CROSSREFS Cf. A000217, A069099, A253878, A253880. Sequence in context: A188685 A052137 A003376 * A309189 A231757 A156975 Adjacent sequences:  A253876 A253877 A253878 * A253880 A253881 A253882 KEYWORD nonn,easy AUTHOR Colin Barker, Jan 17 2015 STATUS approved

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Last modified January 22 05:13 EST 2021. Contains 340360 sequences. (Running on oeis4.)