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 A259750 Numbers that are congruent to {14, 22} mod 24. 7
 14, 22, 38, 46, 62, 70, 86, 94, 110, 118, 134, 142, 158, 166, 182, 190, 206, 214, 230, 238, 254, 262, 278, 286, 302, 310, 326, 334, 350, 358, 374, 382, 398, 406, 422, 430, 446, 454, 470, 478, 494, 502, 518, 526, 542, 550, 566, 574, 590, 598, 614, 622, 638 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Original name: Numbers n such that n/A259748(n) = 2. LINKS Danny Rorabaugh, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA A259748(a(n))/a(n) = 1/2. a(n) = 2*A168489(n) - Danny Rorabaugh, Oct 22 2015 From Colin Barker, Aug 26 2016: (Start) a(n) = a(n-1)+a(n-2)-a(n-3) for n>3. G.f.: 2*x*(7+4*x+x^2) / ((1-x)^2*(1+x)). (End) Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/24 - log(2+sqrt(3))/(4*sqrt(3)). - Amiram Eldar, Dec 31 2021 E.g.f.: 2*(1 + 6*x*exp(x) - exp(-x)). - David Lovler, Sep 06 2022 MATHEMATICA A[n_] := A[n] = Sum[a b, {a, 1, n}, {b, a + 1, n}] ; Select[Range[600], Mod[A[#], #]/# == 1/2 & ] PROG (PARI) vector(100, n, 2*(6*n-(-1)^n)) \\ Altug Alkan, Oct 23 2015 (PARI) Vec(2*x*(7+4*x+x^2)/((1-x)^2*(1+x)) + O(x^100)) \\ Colin Barker, Aug 26 2016 CROSSREFS Cf. A000914, A168489, A259748. Sequence in context: A225710 A183185 A324526 * A211416 A045282 A039291 Adjacent sequences: A259747 A259748 A259749 * A259751 A259752 A259753 KEYWORD nonn,easy AUTHOR José María Grau Ribas, Jul 04 2015 EXTENSIONS Better name from Danny Rorabaugh, Oct 22 2015 STATUS approved

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Last modified July 22 09:18 EDT 2024. Contains 374485 sequences. (Running on oeis4.)