The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A130755 Binomial transform of periodic sequence (3, 1, 2). 10
 3, 4, 7, 15, 32, 65, 129, 256, 511, 1023, 2048, 4097, 8193, 16384, 32767, 65535, 131072, 262145, 524289, 1048576, 2097151, 4194303, 8388608, 16777217, 33554433, 67108864, 134217727, 268435455, 536870912, 1073741825, 2147483649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS The third sequence of "less twisted numbers"; this sequence, A130750 and A130752 form a "suite en trio" (cf. reference, p. 130). First differences of A130752, second differences of A130750. Sequence equals its third differences:   3     4     7    15    32    65   129   256   511  1023      1     3     8    17    33    64   127   255   512         2     5     9    16    31    63   128   257            3     4     7    15    32    65   129 REFERENCES P. Curtz, Exercise Book, manuscript, 1995. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..300 from Vincenzo Librandi) Index entries for linear recurrences with constant coefficients, signature (3,-3,2). FORMULA G.f.: (3-5*x+4*x^2)/((1-2*x)*(1-x+x^2)). a(0) = 3; a(1) = 4; a(2) = 7; for n > 2, a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3). a(n) = 2^(n+1) + A128834(n+2). a(0) = 3; for n > 0, a(n) = 2*a(n-1) + A057079(n+3). MATHEMATICA CoefficientList[Series[(3-5*x+4*x^2)/((1-2*x)*(1-x+x^2)), {x, 0, 50}], x] (* or *) LinearRecurrence[{3, -3, 2}, {3, 4, 7}, 30] (* G. C. Greubel, Jan 15 2018 *) PROG (MAGMA) m:=31; S:=[ [3, 1, 2][(n-1) mod 3 +1]: n in [1..m] ]; [ &+[ Binomial(i-1, k-1)*S[k]: k in [1..i] ]: i in [1..m] ]; // Klaus Brockhaus, Aug 03 2007 (MAGMA) I:=[3, 4, 7]; [n le 3 select I[n] else 3*Self(n-1) - 3*Self(n-2) + 2*Self(n-3): n in [1..30]]; // G. C. Greubel, Jan 15 2018 (PARI) {m=31; v=vector(m); v[1]=3; v[2]=4; v[3]=7; for(n=4, m, v[n]=3*v[n-1]-3*v[n-2]+2*v[n-3]); v} \\ Klaus Brockhaus, Aug 03 2007 (PARI) {for(n=0, 30, print1(2^(n+1)+[1, 0, -1, -1, 0, 1][n%6+1], ", "))} \\ Klaus Brockhaus, Aug 03 2007 CROSSREFS Cf. A010882 (periodic (1, 2, 3)), A128834 (periodic (0, 1, 1, 0, -1, -1)), A057079 (periodic (1, 2, 1, -1, -2, -1)), A130750 (first differences), A130752 (second differences). Sequence in context: A329666 A187493 A027020 * A286348 A116090 A287741 Adjacent sequences:  A130752 A130753 A130754 * A130756 A130757 A130758 KEYWORD nonn,easy AUTHOR Paul Curtz, Jul 13 2007 EXTENSIONS Edited and extended by Klaus Brockhaus, Aug 03 2007 STATUS approved

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

Last modified August 17 03:53 EDT 2022. Contains 356184 sequences. (Running on oeis4.)