A176795 A symmetrical triangle sequence:q=4;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, 37, 1, 1, 361, 361, 1, 1, 3025, 3601, 3025, 1, 1, 24481, 30241, 30241, 24481, 1, 1, 196417, 244801, 254017, 244801, 196417, 1, 1, 1572481, 1964161, 2056321, 2056321, 1964161, 1572481, 1, 1, 12582145, 15724801, 16498945, 16646401

Offset

0,5

Comments

Row sums are:

{1, 2, 39, 724, 9653, 109446, 1136455, 11185928, 106258185, 984268810,...}.

Links

Table of n, a(n) for n=0..40.

Formula

q=4;

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, 37, 1},
{1, 361, 361, 1},
{1, 3025, 3601, 3025, 1},
{1, 24481, 30241, 30241, 24481, 1},
{1, 196417, 244801, 254017, 244801, 196417, 1},
{1, 1572481, 1964161, 2056321, 2056321, 1964161, 1572481, 1},
{1, 12582145, 15724801, 16498945, 16646401, 16498945, 15724801, 12582145, 1},
{1, 100661761, 125821441, 132088321, 133562881, 133562881, 132088321, 125821441, 100661761, 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: A190301 A077575 A215258 * A272725 A057639 A190356

Adjacent sequences: A176792 A176793 A176794 * A176796 A176797 A176798

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Apr 26 2010

Status

approved