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 A156568 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=23, a(2)=115. 3
 23, 115, 667, 3887, 22655, 132043, 769603, 4485575, 26143847, 152377507, 888121195, 5176349663, 30169976783, 175843511035, 1024891089427, 5973503025527, 34816127063735, 202923259356883, 1182723429077563 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..19. Index entries for linear recurrences with constant coefficients, signature (6,-1). FORMULA a(n) = 23*((2+sqrt(2))*(3-2*sqrt(2))^n +(2-sqrt(2))*(3+2*sqrt(2))^n)/4. G.f.: 23*x*(1-x)/(1-6*x+x^2). [corrected by Klaus Brockhaus, Sep 22 2009] Limit_{n -> oo} a(n)/a(n-1) = 3+2*sqrt(2). PROG (PARI) {m=19; v=concat([23, 115], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v} CROSSREFS Second trisection of A156567. Equals 23*A001653. Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156569, A156570. Sequence in context: A111943 A057877 A302530 * A042026 A042028 A265982 Adjacent sequences: A156565 A156566 A156567 * A156569 A156570 A156571 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Feb 11 2009, Feb 16 2009 STATUS approved

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Last modified August 10 18:57 EDT 2024. Contains 375058 sequences. (Running on oeis4.)