A174626 Antidiagonal of sequence: q=5; t(n,m) = Sum((2*cos(i*Pi/q))^m*cos[(m - 2*n)*i*Pi/q), {i, 0, q - 1}]/q.

1, 0, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 3, 5, 0, 1, 1, 3, 5, 11, 1, 0, 2, 2, 6, 10, 22, 0, 1, 1, 3, 5, 11, 21, 43, 0, 1, 1, 3, 5, 11, 21, 43, 85, 1, 0, 2, 2, 6, 10, 22, 42, 86, 170

Offset

0,9

Comments

Row sums are {1, 1, 2, 3, 5, 10, 20, 45, 100, 215, ...}.

References

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, pp. 41.

Links

Table of n, a(n) for n=0..54.

Formula

q=5; t(n,m) = Sum[(2*cos(i*Pi/q))^m*cos((m - 2*n)*i*Pi/q), {i, 0, q - 1}]/q;

out_n,m = Antidiagonal(t(n,m)).

Example

{1},
{0, 1},
{0, 1, 1},
{0, 0, 2, 1},
{0, 0, 1, 3, 1},
{1, 0, 0, 3, 4, 2},
{0, 1, 0, 1, 6, 5, 7},
{0, 1, 1, 0, 4, 10, 7, 22},
{0, 0, 2, 1, 1, 10, 15, 14, 57},
{0, 0, 1, 3, 1, 5, 20, 22, 36, 127}

Mathematica

t[n_, m_, q_] = Sum[(2*Cos[i*Pi/q])^m*Cos[(m - 2*n)*i*Pi/q], {i, 0, q - 1}]/q;
a = Table[Table[If[ Rationalize[ N[t[n, m, q]]] < 10^(-10), 0, Rationalize[N[t[n, m, q]]]], {m, 0, 10}, {n, 0, 10}], {q, 3, 10, 2}];
Table[Flatten[Table[Table[a[[l]][[m, n - m + 1]], {m, 1, n}], {n, 1, 10}]], {l, 1, Length[a]}]

Crossrefs

Sequence in context: A279006 A112555 A108561 * A264909 A104579 A079531

Adjacent sequences: A174623 A174624 A174625 * A174627 A174628 A174629

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 24 2010

Status

approved