A175353 Antidiagonal expansion of (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).

2, 6, 1, 18, 3, 1, 54, 7, 2, 1, 162, 17, 5, 2, 1, 486, 41, 11, 4, 2, 1, 1458, 99, 24, 9, 4, 2, 1, 4374, 239, 53, 19, 8, 4, 2, 1, 13122, 577, 117, 40, 17, 8, 4, 2, 1

Offset: 0

Author

Roger L. Bagula, Dec 03 2010

Keywords

• nonn
• tabl

Comments

Row sums are {0, 2, 7, 22, 64, 187, 545, 1597, 4700, 13888, ...};

I reversed the signs on Riordan's Fibonacci function.

Examples

			{2},
{6, 1},
{18, 3, 1},
{54, 7, 2, 1},
{162, 17, 5, 2, 1},
{486, 41, 11, 4, 2, 1},
{1458, 99, 24, 9, 4, 2, 1},
{4374, 239, 53, 19, 8, 4, 2, 1},
{13122, 577, 117, 40, 17, 8, 4, 2, 1}
		

References

• J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 125 and 155.

Crossrefs

Cf. A175331.

Programs

Mathematica

f[x_, n_] = (x + x^(m + 1))/(1 - 2*x - x^(m + 1));
a = Table[Table[SeriesCoefficient[
      Series[f[x, m], {x, 0, 10}], n], {n, 0, 10}], {m, 0, 10}];
Table[Table[a[[m, n - m + 1]], {m, 1, n - 1}], {n, 1, 10}];
Flatten[%]

Formula

G.f.: f(x,m) = (x + x^(m + 1))/(1 - 2*x - x^(m + 1)).