A193631 Augmentation of the triangle given by p(n,k)=(3+(-1)^k)/2 for 0<=k<=n. See Comments.

1, 2, 1, 4, 4, 5, 8, 12, 22, 17, 16, 32, 72, 88, 89, 32, 80, 208, 328, 474, 417, 64, 192, 560, 1056, 1836, 2364, 2253, 128, 448, 1440, 3120, 6168, 9684, 13038, 11937, 256, 1024, 3584, 8704, 19040, 34240, 54800, 71152, 66737, 512, 2304, 8704, 23296

Offset

0,2

Comments

For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.

(column 2 of A193631)=A001787.

Links

Table of n, a(n) for n=0..48.

Example

First five rows of the triangle P=p(n,k):
2
2...1
2...1...2
2...1...2...1
2...1...2...1...2
First five rows of A193631:
1
2....1
4....4....5
8....12...22...17
16...32...72...88...89

Mathematica

p[n_, k_] := (3 + (-1)^k)/2;
Table[p[n, k], {n, 0, 7}, {k, 0, n}]
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193631 *)
Flatten[Table[v[n], {n, 0, 8}]]

Crossrefs

Cf. A193091, A001787.

Sequence in context: A101452 A019963 A165417 * A190993 A326147 A351168

Adjacent sequences: A193628 A193629 A193630 * A193632 A193633 A193634

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 01 2011

Status

approved