A176793 A symmetrical triangle:q=2;f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q)))

1, 1, 1, 1, 5, 1, 1, 25, 25, 1, 1, 113, 145, 113, 1, 1, 481, 673, 673, 481, 1, 1, 1985, 2881, 3137, 2881, 1985, 1, 1, 8065, 11905, 13441, 13441, 11905, 8065, 1, 1, 32513, 48385, 55553, 57601, 55553, 48385, 32513, 1, 1, 130561, 195073, 225793, 238081, 238081

Offset

0,5

Comments

Row sums are:

{1, 2, 7, 52, 373, 2310, 12871, 66824, 330505, 1579018,...}.

Links

Table of n, a(n) for n=0..50.

Formula

q=2;

f(n,m,q)=Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];

t(n,m,q)=1 - (f(n, k, q) + f(n, 2*n - k, q) - (f(n, 1, q) + f(n, 2*n - 1, q)))

Example

{1},
{1, 1},
{1, 5, 1},
{1, 25, 25, 1},
{1, 113, 145, 113, 1},
{1, 481, 673, 673, 481, 1},
{1, 1985, 2881, 3137, 2881, 1985, 1},
{1, 8065, 11905, 13441, 13441, 11905, 8065, 1},
{1, 32513, 48385, 55553, 57601, 55553, 48385, 32513, 1},
{1, 130561, 195073, 225793, 238081, 238081, 225793, 195073, 130561, 1}

Mathematica

f[n_, k_, q_] := Sum[q^((k - 1)/2)*Binomial[n, m], {m, 1, n, 2}];
t[n_, k_, q_] := 1 - (f[n, k, q] + f[n, 2*n - k, q] - (f[n, 1, q] + f[n, 2* n - 1, q]));
Table[Flatten[Table[Table[t[ n, k, q], {k, 1, 2*n, 2}], {n, 1, 10}]], {q, 2, 10}]

Crossrefs

Sequence in context: A329118 A152572 A203346 * A118190 A172342 A143213

Adjacent sequences: A176790 A176791 A176792 * A176794 A176795 A176796

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 26 2010

Status

approved