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
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
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
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