This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117575 Expansion of (1-x^3)/((1-x)*(1+2*x^2)). 3
 1, 1, -1, -2, 2, 4, -4, -8, 8, 16, -16, -32, 32, 64, -64, -128, 128, 256, -256, -512, 512, 1024, -1024, -2048, 2048, 4096, -4096, -8192, 8192, 16384, -16384, -32768, 32768, 65536, -65536, -131072, 131072, 262144, -262144, -524288, 524288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums of A116949. From Paul Curtz, Oct 24 2012: (Start) b(n)=abs (a(n))=A158780(n+1)=1,1,1,2,2,4,4,8,8,8,... . Consider the autosequence (that is a sequence whose inverse binomial transform is equal to the signed sequence) of the first kind of the example. Its numerator is A046978(n), its denominator is b(n). The numerator of the first column is A075553(n). The denominator corresponding to the 0's is a choice. The classical denominator is 1,1,1,2,1,4,4,8,1,16,16,32,1,... . (End) LINKS Index entries for linear recurrences with constant coefficients, signature (0,-2). FORMULA a(n) = a(n-1)-2*a(n-2)+2*a(n-3), n>=3; a(n) = (cos(pi*/2)+sin(pi*n/2)) * (2^((n-1)/2)*(1-(-1)^n)/2 + 2^((n-2)/2)*(1+(-1)^n)/2 + 0^n/2). a(n+1) = Sum_{k, 0<=k<=n} A122016(n,k)*(-1)^k. - Philippe Deléham, Jan 31 2012 EXAMPLE 0/1,  1/1    1/1,  1/2,   0/2,  -1/4,  -1/4,  -1/8,... 1/1,   0/1,  -1/2, -1/2,  -1/4,   0/4,   1/8,   1/8,... -1/1, -1/2,   0/2,  1/4,   1/4,   1/8,   0/8,  -1/16,... 1/2,   1/2,   1/4,  0/4   -1/8,  -1/8,  -1/16,  0/16,... 0/2,  -1/4,  -1/4, -1/8,   0/8,   1/16,  1/16,  1/32,... -1/4,  0/4,   1/8,  1/8,   1/16,  0/16, -1/32, -1/32,... 1/4,   1/8,   0/8, -1/16, -1/16, -1/32,  0/32,  1/64,... -1/8, -1/8,  -1/16, 0/16,  1/32,  1/32,  1/64,  0/64. - Paul Curtz, Oct 24 2012 MATHEMATICA CoefficientList[Series[(1-x^3)/((1-x)(1+2 x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, -2}, {1, 1, -1}, 45] (* Harvey P. Dale, Apr 09 2018 *) PROG (PARI) a(n)=if(n, (-1)^(n\2)<<((n-1)\2), 1) \\ Charles R Greathouse IV, Jan 31 2012 CROSSREFS Cf. A016116, A191754/A192366. Sequence in context: A082267 A076939 A158780 * A131572 A152166 A320770 Adjacent sequences:  A117572 A117573 A117574 * A117576 A117577 A117578 KEYWORD easy,sign AUTHOR Paul Barry, Mar 29 2006 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 18 18:56 EDT 2019. Contains 328197 sequences. (Running on oeis4.)