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 A261064 a(n) = (3^n-1)*(n+1)/4. 5
 1, 6, 26, 100, 363, 1274, 4372, 14760, 49205, 162382, 531438, 1727180, 5580127, 17936130, 57395624, 182948560, 581130729, 1840247318, 5811307330, 18305618100, 57531942611, 180441092746, 564859072956, 1765184603000, 5507375961373, 17157594341214 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Second column of A201730. Number of non-selfintersecting broken lines in a convex (n+1)-gon. (National Math Contest "Atanas Radev" 2020, Bulgaria) - Ivaylo Kortezov, Jan 18 2020 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..1000 National Math Contest "Atanas Radev", Problems and Solutions, problem 8.4 ("Задача 8.4" in Bulgarian), Jan 2020. Index entries for linear recurrences with constant coefficients, signature (8,-22,24,-9). FORMULA G.f.: -x*(-1 + 2*x) / ( (3*x - 1)^2*(x - 1)^2 ). a(n) = A212337(n - 1) - 2*A212337(n - 2). a(n) = Sum_{k = 1..n} A027907(n, 2k - 1)*k . - J. Conrad, Aug 30 2016 a(n) = Sum_{k = 0..(n - 1)} binomial(n + 1, k + 2)*A001792(k). - Ivaylo Kortezov, Jan 21 2020 MATHEMATICA LinearRecurrence[{8, -22, 24, -9}, {1, 6, 26, 100}, 30] (* Vincenzo Librandi, Aug 31 2016 *) Table[(3^n - 1)(n + 1)/4, {n, 0, 39}] (* Alonso del Arte, Jan 19 2020 *) PROG (PARI) first(m)=vector(m, i, (3^i-1)*(i+1)/4); /* Anders Hellström, Aug 08 2015 */ (Magma) [(3^n-1)*(n+1)/4: n in [1..30]]; // Vincenzo Librandi, Aug 31 2016 CROSSREFS Cf. A001792, A027907, A201730, A212337. Sequence in context: A055420 A137746 A344504 * A094811 A005022 A125107 Adjacent sequences: A261061 A261062 A261063 * A261065 A261066 A261067 KEYWORD nonn,easy AUTHOR R. J. Mathar, Aug 08 2015 STATUS approved

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Last modified February 27 08:19 EST 2024. Contains 370367 sequences. (Running on oeis4.)