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A072262
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a(n) = 4*a(n-1) + 1, a(1)=11.
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4
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11, 45, 181, 725, 2901, 11605, 46421, 185685, 742741, 2970965, 11883861, 47535445, 190141781, 760567125, 3042268501, 12169074005, 48676296021, 194705184085, 778820736341, 3115282945365, 12461131781461, 49844527125845
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OFFSET
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1,1
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COMMENTS
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These are the integers N which on application of the Collatz function yield the number 17. 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 17).
Numbers whose binary representation is 1011 together with n - 1 times 01. For example, a(4) = 725 = 1011010101 (2). - Omar E. Pol, Nov 24 2012
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LINKS
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G. C. Greubel, 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
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FORMULA
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From Bruno Berselli, Dec 16 2011: (Start)
G.f.: x*(11-10*x)/(1-5*x+4*x^2).
a(n) = (17*2^(2*n-1) - 1)/3.
Sum_{i=1..n} a(i) = (a(n+1) - n + 1)/3 - 4. (End)
a(n) = 34*A002450(n-1) + 11 . - Yosu Yurramendi, Jan 24 2017
E.g.f.: (-15 - 2*exp(x) + 17*exp(4*x))/6. - G. C. Greubel, Jan 14 2020
a(n) = A178415(6, n) = A347834(5, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021
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MAPLE
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seq( (17*4^n -2)/6, n=1..30); # G. C. Greubel, Jan 14 2020
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MATHEMATICA
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a[n_]:= 4a[n-1] +1; a[1]=11; Table[a[n], {n, 25}]
NestList[4#+1&, 11, 30] (* or *) LinearRecurrence[{5, -4}, {11, 45}, 30] (* Harvey P. Dale, Dec 25 2014 *)
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PROG
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(PARI) vector(30, n, (17*4^n -2)/6) \\ G. C. Greubel, Jan 14 2020
(Magma) [(17*4^n -2)/6: n in [1..30]]; // G. C. Greubel, Jan 14 2020
(Sage) [(17*4^n -2)/6 for n in (1..30)] # G. C. Greubel, Jan 14 2020
(GAP) List([1..30], n-> (17*4^n -2)/6); # G. C. Greubel, Jan 14 2020
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CROSSREFS
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Cf. A072257, A072258, A072259, A072260, A072261, A099730, A178415, A347834.
Sequence in context: A051740 A263227 A144932 * A231224 A231438 A322560
Adjacent sequences: A072259 A072260 A072261 * A072263 A072264 A072265
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KEYWORD
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nonn,easy
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AUTHOR
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N. Rathankar (rathankar(AT)yahoo.com), Jul 08 2002
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EXTENSIONS
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Edited and extended by Robert G. Wilson v, Jul 17 2002
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STATUS
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approved
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