Re: recursion won't work for some reason

*To*: mathgroup at smc.vnet.net*Subject*: [mg124861] Re: recursion won't work for some reason*From*: "Harvey P. Dale" <hpd1 at nyu.edu>*Date*: Thu, 9 Feb 2012 05:44:17 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201202070901.EAA23387@smc.vnet.net> <201202081033.FAA06582@smc.vnet.net>

This is a perfect problem for LinearRecurrence: LinearRecurrence[{0,0,-1,0,0,21,0,0,69,0,0,64},{1,1,1,5,4,3,25,23,22,149 ,130,110},30] Best, Harvey -----Original Message----- From: Bob Hanlon [mailto:hanlonr357 at gmail.com] Sent: Wednesday, February 08, 2012 5:34 AM To: mathgroup at smc.vnet.net Subject: [mg124861] Re: recursion won't work for some reason Use Set ( = ) rather than Equal ( == ) to initialize the sequence. 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_Integer?Positive] := a[n] = 64*a[-12 + n] + 69*a[-9 + n] + 21*a[-6 + n] - a[-3 + n] Table[a[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 } Bob Hanlon On Tue, Feb 7, 2012 at 4:01 AM, Roger Bagula <roger.bagula 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. > -- Bob Hanlon

**References**:**recursion won't work for some reason***From:*Roger Bagula <roger.bagula@gmail.com>

**Re: recursion won't work for some reason***From:*Bob Hanlon <hanlonr357@gmail.com>