three parallel methods for one sequence : Hermite like recurance
- To: mathgroup at smc.vnet.net
- Subject: [mg69432] three parallel methods for one sequence : Hermite like recurance
- From: Roger Bagula <rlbagula at sbcglobal.net>
- Date: Tue, 12 Sep 2006 06:53:09 -0400 (EDT)
Vector Matrix Markov, HermiteH and recursion all give the same sequence : A062267 M := {{0, 1}, {-2*(n - 1), 2} } v[1] = {1, 2}; v[n_] := v[n] = M.v[n - 1] a0 = Table[v[n][[1]], {n, 1, 30}] Table[HermiteH[n, 1], {n, 0, 30}] a[0] = 1; a[1] = 2; a[n_] := a[n] = 2*(a[n - 1] - (n - 1)*a[n - 2]) b = Table[a[n], {n, 0, 30}] {1, 2, 2, -4, -20, -8, 184, 464, -1648, -10720, 8224, 230848, 280768, -4978816, -17257600, 104891648, 727511296, -1901510144, -28538404352, 11377556480, 1107214478336, 1759326697472, -42984354695168, -163379084079104, 1650522147819520, 11143240331436032, -60239626728103936, -699927750690881536, 1853084341935849472, 42902122722561064960, -21674646387157139456} TrueQ[a1 == a0] TrueQ[b == a1] True True