A176794 A symmetrical triangle sequence:q=3;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, 17, 1, 1, 129, 129, 1, 1, 833, 1025, 833, 1, 1, 5121, 6657, 6657, 5121, 1, 1, 30977, 40961, 43265, 40961, 30977, 1, 1, 186369, 247809, 266241, 266241, 247809, 186369, 1, 1, 1119233, 1490945, 1610753, 1638401, 1610753, 1490945, 1119233, 1, 1

Offset

0,5

Comments

Row sums are:

{1, 2, 19, 260, 2693, 23558, 187143, 1400840, 10080265, 70549514,...}.

Links

Table of n, a(n) for n=0..45.

Formula

q=3;

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, 17, 1},
{1, 129, 129, 1},
{1, 833, 1025, 833, 1},
{1, 5121, 6657, 6657, 5121, 1},
{1, 30977, 40961, 43265, 40961, 30977, 1},
{1, 186369, 247809, 266241, 266241, 247809, 186369, 1},
{1, 1119233, 1490945, 1610753, 1638401, 1610753, 1490945, 1119233, 1},
{1, 6717441, 8953857, 9691137, 9912321, 9912321, 9691137, 8953857, 6717441, 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: A218115 A144442 A157151 * A176244 A022180 A156581

Adjacent sequences: A176791 A176792 A176793 * A176795 A176796 A176797

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 26 2010

Status

approved