This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A192307 0-sequence of reduction of (3n) by x^2 -> x+1. 2
 3, 3, 12, 24, 54, 108, 213, 405, 756, 1386, 2508, 4488, 7959, 14007, 24492, 42588, 73698, 126996, 218025, 373065, 636468, 1082958, 1838232, 3113424, 5262699, 8879403, 14956428, 25153440, 42241806, 70844796 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS See A192232 for definition of "k-sequence of reduction of [sequence] by [substitution]". LINKS FORMULA a(n) = 3*A190062(n). G.f.: 3*x*(1-2*x+2*x^2)/(1-x)/(1-x-x^2)^2. [Colin Barker, Feb 11 2012] MATHEMATICA c[n_] := 3 n; (*  *) Table[c[n], {n, 1, 15}] q[x_] := x + 1; p[0, x_] := 3; p[n_, x_] := p[n - 1, x] + (x^n)*c[n + 1] reductionRules = {x^y_?EvenQ -> q[x]^(y/2),    x^y_?OddQ -> x q[x]^((y - 1)/2)}; t = Table[   Last[Most[     FixedPointList[Expand[#1 /. reductionRules] &, p[n, x]]]], {n, 0,    30}] Table[Coefficient[Part[t, n], x, 0], {n, 1, 30}]  (* A192307 *) Table[Coefficient[Part[t, n]/3, x, 0], {n, 1, 30}]  (* A190062 *) Table[Coefficient[Part[t, n], x, 1], {n, 1, 30}]  (* A192308 *) Table[Coefficient[Part[t, n]/3, x, 1], {n, 1, 30}]  (* A122491 *) (* by Peter J. C. Moses, Jun 20 2011 *) CROSSREFS Cf. A192232, A192307. Sequence in context: A268798 A136533 A268639 * A161804 A097342 A025236 Adjacent sequences:  A192304 A192305 A192306 * A192308 A192309 A192310 KEYWORD nonn,easy,changed AUTHOR Clark Kimberling, Jun 27 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 09:29 EST 2016. Contains 278849 sequences.