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 A072261 a(n) = 4*a(n-1) + 1, a(1)=7. 8
 7, 29, 117, 469, 1877, 7509, 30037, 120149, 480597, 1922389, 7689557, 30758229, 123032917, 492131669, 1968526677, 7874106709, 31496426837, 125985707349, 503942829397, 2015771317589, 8063085270357, 32252341081429, 129009364325717, 516037457302869 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are the integers N which on application of the Collatz function yield the number 11. The Collatz function: if N is an odd number then (3N+1)/2^r yields a positive odd integer for some value of r (which in this case is 11). These numbers reach 11 in Collatz function iteration after 2(n+1) steps and so end in 1 after exactly 2n+18 steps. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004 Numbers whose binary representation is 111 together with n - 1 times 01. For example, a(4) = 469 = 111010101 (2). - Omar E. Pol, Nov 24 2012 LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (5,-4). Index entries for sequences related to 3x+1 (or Collatz) problem FORMULA a(n) = (11*4^n - 2)/6 = 22*A002450(n-1) + 7. - Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 08 2004 From Colin Barker, Oct 27 2019: (Start) G.f.: x*(7 - 6*x) / ((1 - x)*(1 - 4*x)). a(n) = 5*a(n-1) - 4*a(n-2) for n>2. (End) E.g.f.: (-9 - 2*exp(x) + 11*exp(4*x))/6. - G. C. Greubel, Jan 14 2020 a(n) = a(n-1) + 11*2^(2*n-3), for n >= 2, with a(1) = 7. - Wolfdieter Lang, Aug 16 2021 a(n) = A178415(4, n) = A347834(3, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021 MAPLE seq(coeff(series(x*(7-6*x)/((1-x)*(1-4*x)), x, n+1), x, n), n = 1..25); # G. C. Greubel, Jan 14 2020 MATHEMATICA a[n_]:= 4a[n-1] +1; a[1]=7; Table[a[n], {n, 25}] NestList[4#+1&, 7, 30] (* or *) LinearRecurrence[{5, -4}, {7, 29}, 30] (* Harvey P. Dale, Sep 04 2023 *) PROG (PARI) Vec(x*(7-6*x)/((1-x)*(1-4*x)) + O(x^25)) \\ Colin Barker, Oct 27 2019 (Magma) [(11*4^n -2)/6: n in [1..25]]; // G. C. Greubel, Jan 14 2020 (Sage) [(11*4^n -2)/6 for n in (1..25)] # G. C. Greubel, Jan 14 2020 (GAP) List([1..25], n-> (11*4^n -2)/6); # G. C. Greubel, Jan 14 2020 CROSSREFS Cf. A002450, A072197, A072257, A072258, A072259, A072260, A072262, A099730, A178415, A347834. Sequence in context: A296646 A037094 A118171 * A066744 A037576 A327587 Adjacent sequences: A072258 A072259 A072260 * A072262 A072263 A072264 KEYWORD nonn,easy AUTHOR N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002 EXTENSIONS Edited and extended by Robert G. Wilson v, Jul 17 2002 More terms from Colin Barker, Oct 27 2019 STATUS approved

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Last modified September 11 16:20 EDT 2024. Contains 375836 sequences. (Running on oeis4.)