0,5

Row sums are: {1, 2, 8, 32, 44, 112, 248, 632, 764, 1568, 3248,...}. The k is added to give a quantum level to the resulting symmetrical functions.

t(n,m)=Binomial[n,m]+p(n,m);

k=2;

p(n,m)=If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k* Binomial[n, m], 0]].

{1},

{1, 1},

{1, 6, 1},

{1, 15, 15, 1},

{1, 12, 18, 12, 1},

{1, 25, 30, 30, 25, 1},

{1, 18, 75, 60, 75, 18, 1},

{1, 35, 105, 175, 175, 105, 35, 1},

{1, 24, 84, 168, 210, 168, 84, 24, 1},

{1, 45, 108, 252, 378, 378, 252, 108, 45, 1},

{1, 30, 225, 360, 630, 756, 630, 360, 225, 30, 1}

Clear[p];

k=2;

p[n_, m_] = If[Mod[Binomial[n, m], 2] == 0, 2^(k - 1)*Binomial[n, m], If[Mod[Binomial[n, m], 2] == 1 && Binomial[n, m] > 1, 2^k*Binomial[n, m], 0]];

Table[Table[Binomial[n, m] + p[n, m], {m, 0, n}], {n, 0, 10}];

Flatten[%]

Sequence in context: A146772 A082105 A143210 this_sequence A086645 A168291 A154980

Adjacent sequences: A152235 A152236 A152237 this_sequence A152239 A152240 A152241

nonn

Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 30 2008