login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A193631 Augmentation of the triangle given by p(n,k)=(3+(-1)^k)/2 for 0<=k<=n.  See Comments. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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 A196082

Adjacent sequences:  A193628 A193629 A193630 * A193632 A193633 A193634

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 01 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)