login
A261671
If n even, a(n) = 6n+3, otherwise a(n) = n.
4
3, 1, 15, 3, 27, 5, 39, 7, 51, 9, 63, 11, 75, 13, 87, 15, 99, 17, 111, 19, 123, 21, 135, 23, 147, 25, 159, 27, 171, 29, 183, 31, 195, 33, 207, 35, 219, 37, 231, 39, 243, 41, 255, 43, 267, 45, 279, 47, 291, 49, 303, 51, 315, 53, 327, 55, 339, 57, 351, 59, 363
OFFSET
0,1
COMMENTS
Although the OEIS indexes sequences by consecutive integers, it is better to think of this sequence as defined on the odd numbers 1,3,5,7,... and given by f(4m+1)=12m+3, f(4m+3)=2m+1, that is, subtract 1 and divide by 2 if the result is odd, otherwise multiply by 3. This arises in analyzing A109732.
It is conjectured that starting with any positive odd number d and iterating f, we always eventually reach either 1, 9, or 33 (see Comments in A135730).
FORMULA
From Colin Barker, Sep 13 2015: (Start)
a(n) = (3+3*(-1)^n+7*n+5*(-1)^n*n)/2.
a(n) = 2*a(n-2) - a(n-4) for n>3.
G.f.: (x^3+9*x^2+x+3) / ((x-1)^2*(x+1)^2).
(End)
MATHEMATICA
Table[If[EvenQ[n], 6n+3, n], {n, 0, 60}] (* or *) LinearRecurrence[{0, 2, 0, -1}, {3, 1, 15, 3}, 70] (* Harvey P. Dale, Dec 30 2023 *)
PROG
(PARI) Vec((x^3+9*x^2+x+3)/((x-1)^2*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 13 2015
CROSSREFS
Sequence in context: A134146 A085569 A336454 * A198148 A286674 A286024
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 02 2015
STATUS
approved