editing

approved

_Roger L. Bagula (rlbagulatftn(AT)yahoo.com), _, Mar 05 2010

approved

editing

proposed

approved

editing

proposed

Roger L. Bagula and Geoffrey Critzer (rlbagulatftn(AT)yahoo.com), Mar 05 2010

approved

editing

A triangle based on:a(n,q)=a(n-1,q)+q*a(n-2,q);t(n,q)=If[n == 0, 1, Sum[Binomial[n, k]*a(k, q), {k, 1, n, 2}]]

1, 1, 1, 2, 1, 1, 5, 2, 1, 1, 12, 6, 2, 1, 1, 30, 16, 7, 2, 1, 1, 76, 46, 20, 8, 2, 1, 1, 195, 132, 64, 24, 9, 2, 1, 1, 504, 386, 200, 84, 28, 10, 2, 1, 1, 1309, 1136, 643, 280, 106, 32, 11, 2, 1, 1

0,4

Row sums are:

{1, 2, 4, 9, 22, 57, 154, 428, 1216, 3521,...}.

a(n,q)=a(n-1,q)+q*a(n-2,q);

t(n,q)=If[n == 0, 1, Sum[Binomial[n, k]*a(k, q), {k, 1, n, 2}]]

{1},

{1, 1},

{2, 1, 1},

{5, 2, 1, 1},

{12, 6, 2, 1, 1},

{30, 16, 7, 2, 1, 1},

{76, 46, 20, 8, 2, 1, 1},

{195, 132, 64, 24, 9, 2, 1, 1},

{504, 386, 200, 84, 28, 10, 2, 1, 1},

{1309, 1136, 643, 280, 106, 32, 11, 2, 1, 1}

Clear[t, n, q, a];

f[0, a_] := 0; f[1, a_] := 1;

f[n_, a_] := f[n, a] = f[n - 1, a] + a*f[n - 2, a];

t[n_, q_] = If[n == 0, 1, Sum[Binomial[n, k]*f[k, q], {k, 1, n, 2}]];

a = Table[Table[t[n, q], {n, 0, 10}], {q, 1, 11}];

Table[Table[a[[m, n - m + 1]], {m, 1, n}], {n, 1, 10}];

Flatten[%]

nonn,tabl,uned

Roger L. Bagula and Geoffrey Critzer (rlbagulatftn(AT)yahoo.com), Mar 05 2010

approved