Re: number pattern sequence tia sal2

*To*: mathgroup at smc.vnet.net*Subject*: [mg85398] Re: [mg85379] number pattern sequence tia sal2*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Sat, 9 Feb 2008 04:13:49 -0500 (EST)*References*: <1963121.1202472573313.JavaMail.root@m08>*Reply-to*: drmajorbob at bigfoot.com

list = {3, 8, 4, 9, 5, 1, 6, 2, 7}; Column[Table[(-1)^n Differences[list, n], {n, 0, -1 + Length@list}]] {3,8,4,9,5,1,6,2,7} {-5,4,-5,4,4,-5,4,-5} {-9,9,-9,0,9,-9,9} {-18,18,-9,-9,18,-18} {-36,27,0,-27,36} {-63,27,27,-63} {-90,0,90} {-90,-90} {0} Clear[poly] poly[data_] := Module[{differences = First /@ NestList[Rest@# - Most@# &, data, Length@data - 1]}, differences.Table[ Binomial[x - 1, k], {k, 0, Length@data - 1}] // Expand ] one[x_] = poly[list] Array[one, Length@list] -128 + (5407 x)/20 - (1545 x^2)/8 + (501 x^3)/8 - (75 x^4)/8 + ( 21 x^5)/40 - 90 Binomial[-1 + x, 6] + 90 Binomial[-1 + x, 7] {3, 8, 4, 9, 5, 1, 6, 2, 7} two[x_] = Expand@InterpolatingPolynomial[list, x] Array[two, Length@list] -308 + (101389 x)/140 - (5045 x^2)/8 + (2203 x^3)/8 - (265 x^4)/4 + ( 89 x^5)/10 - (5 x^6)/8 + x^7/56 {3, 8, 4, 9, 5, 1, 6, 2, 7} Bobby On Thu, 07 Feb 2008 21:30:56 -0600, <ratullochjk at gmail.com> wrote: > Greetings All > > I'm having some trouble figuring out a sequence of numbers using commo= n > Difference. > I've figured out the polynomial for the even numbers for the sequence > but the odd numbers have a repeating pattern which I'm not sure how to= > create a Polynomial for. > > I've included my work here > http://demos.onewithall.net/number_patterns.jpg on the even numbers > which I've verified and they are correct. > > I've included the odd numbers also I started doing the sequence of > numbers using common Difference but as you can see I get a pattern of > repeating numbers (-5,4). > > How can I go about getting the polynomial for the odd numbers like I > did for the even ones. > > > Tia sal2 > > -- = DrMajorBob at bigfoot.com