A144409 Antidiagonal expansion of: f(t,n) = If[n == 1, 1/(1 - t), 1/(1 - t^floor(n/2) - t^n)].

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0, 1, 3, 1, 1, 0, 1, 2, 5, 1, 1, 0, 1, 0, 3, 8, 1, 1, 0, 0, 0, 2, 4, 13, 1, 1, 0, 0, 1, 1, 0, 6, 21, 1, 1, 0, 0, 1, 0, 1, 3, 9, 34, 1, 1, 0, 0, 0, 0, 0, 1, 0, 13, 55, 1, 1, 0, 0, 0, 1, 0, 2, 2, 5, 19, 89, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 28, 144, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 3

Offset

1,9

Comments

Row sums are {1, 2, 3, 5, 6, 10, 14, 21, 31, 50, 71, 120, 177, 288, 445}.

Links

Table of n, a(n) for n=1..101.

Formula

f(t,n) = If[n == 1, 1/(1 - t), 1/(1 - t^floor(n/2) - t^n)); t(n,m) = antidiagonal_expansion(f(t,n)).

Example

{1},
{1, 1},
{1, 1, 1},
{1, 1, 2, 1},
{1, 0, 1, 3, 1},
{1, 0, 1, 2, 5, 1},
{1, 0, 1, 0, 3, 8, 1},
{1, 0, 0, 0, 2, 4, 13, 1},
{1, 0, 0, 1, 1, 0, 6, 21, 1},
{1, 0, 0, 1, 0, 1, 3, 9, 34, 1},
{1, 0, 0, 0, 0, 0, 1, 0, 13, 55, 1},
{1, 0, 0, 0, 1, 0, 2, 2, 5, 19, 89, 1},
{1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 28, 144, 1},
{1, 0, 0, 0, 0, 0, 0, 1, 0, 3, 8, 41, 233, 1},
{1, 0, 0, 0, 0, 1, 0, 0, 0, 3, 2, 0, 60, 377, 1}

Mathematica

f[t_, n_] = If[n == 1, 1/(1 - t), 1/(1 - t^Floor[n/2] - t^n)]; a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}]; b = Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}] ; Flatten[b]

Crossrefs

Cf. A099238.

Sequence in context: A027052 A322508 A194438 * A131257 A105806 A129501

Adjacent sequences: A144406 A144407 A144408 * A144410 A144411 A144412

Keyword

nonn,uned

Author

Roger L. Bagula and Gary W. Adamson, Sep 30 2008

Status

approved