Re: recursion won't work for some reason

*To*: mathgroup at smc.vnet.net*Subject*: [mg124841] Re: recursion won't work for some reason*From*: Dana DeLouis <dana01 at me.com>*Date*: Thu, 9 Feb 2012 05:37:18 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

> Table[f[n], {n, 1, 30}] Hi. I see you have a solution with Set, and not Equal. Just to mention an alternative to using Table. data = {1 ,1 ,1 ,5 ,4 ,3 ,25 ,23 ,22 ,149 ,130 ,110}; k = {0 ,0 ,-1 ,0 ,0 ,21 ,0 ,0 ,69 ,0 ,0 ,64}; LinearRecurrence[k , data , 30] {1 ,1 ,1 ,5 ,4 ,3 ,25 ,23 ,22 ,149 ,130 ,110 , 785 ,693 ,623 ,4389 ,3880 ,3397 ,23977 , 21115 ,18684 ,131893 ,116502 ,102680 , 724705 ,638985 ,563949 ,3980357 ,3512812 ,3098935} = = = = = = = = = = = = = HTH :>) Dana DeLouis Mac & Math 8 = = = = = = = = = = = = = On Feb 7 , 4:02 am, Roger Bagula <roger.bag... at gmail.com> wrote: > This recursion is translated from a FindSequenceFunction[]: > won't work in version 8? > Clear[a, n] > a[1] == 1; a[2] == 1; a[3] == 1; a[4] == 5; a[5] == 4; a[6] == 3; > a[7] == 25; a[8] == 23; a[9] == 22; a[10] == 149; a[11] == 130; > a[12] == 110; > a[n_] := a[n] = > 64* a[-12 + n] + 69 *a[-9 + n] + 21 *a[-6 + n] - a[-3 + n] > Table[a[n], {n, 1, 30}] > I actually have hundreds like this that work with no problems...from > version 5 and before. > The FindSequenceFunction is: > f[n_] = FindSequenceFunction[{1, 1, 1, 5, 4, 3, 25, 23, 22, 149, 130, > 110, 785, 693, 623, 4389, 3880, 3397, 23977, 21115, 18684, 131893, > 116502, 102680, 724705, 638985, 563949, 3980357, 3512812, 3098935, > 21873593, 19295871, 17024690, 120159701, 106019274, 93536946, > 660211505, 582473085, 513900795, 3627162981, 3200166736, > 2823410521, 19928207945, 17582033699, 15512135608, 109487029365, > 96597344158, 85225004732, 601533119489, 530715145745, > 468234819865}, n] > Table[f[n], {n, 1, 30}] > {1, 1, 1, 5, 4, 3, 25, 23, 22, 149, 130, 110, 785, 693, 623, 4389, > 3880, 3397, 23977, 21115, 18684, 131893, 116502, 102680, 724705, > 638985, 563949, 3980357, 3512812, 3098935} > > The original sequence is a polynomial expansion: > q[x_] = (-2 + 3 x - 8 x^3 + 8 x^4) > f[x_] = ExpandAll[x^4*q[1/x]] > a = Table[8^(1 + Floor[n/3])*SeriesCoefficient[ > Series[1/f[x], {x, 0, 50}], n], {n, 0, 50}] > > Any help that you can give will be appreciated.