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MathGroup Archive 2006

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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


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