login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A147289 A multi-shifted and scaled Pascal triangle: t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}]. 0
1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 6, 12, 6, 1, 1, 7, 18, 18, 7, 1, 1, 8, 25, 38, 25, 8, 1, 1, 9, 33, 63, 63, 33, 9, 1, 1, 10, 42, 96, 128, 96, 42, 10, 1, 1, 11, 52, 138, 224, 224, 138, 52, 11, 1, 1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are: {1, 2, 6, 12, 26, 52, 106, 212, 426, 852, 1706, ...}.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

t(n,m)=Binomial[n, m] + Sum[If[n >= 2*k,2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}].

EXAMPLE

{1}, {1, 1}, {1, 4, 1}, {1, 5, 5, 1}, {1, 6, 12, 6, 1}, {1, 7, 18, 18, 7, 1}, {1, 8, 25, 38, 25, 8, 1}, {1, 9, 33, 63, 63, 33, 9, 1}, {1, 10, 42, 96, 128, 96, 42, 10, 1}, {1, 11, 52, 138, 224, 224, 138, 52, 11, 1}, {1, 12, 63, 190, 362, 450, 362, 190, 63, 12, 1}

MATHEMATICA

Table[Binomial[n, m] + Sum[If[n >= 2*k, 2*Binomial[n - 2*k, m - k], 0], {k, 1, Floor[n/2]}], {n, 0, 10}, {m, 0, n}]; Flatten[%]

CROSSREFS

Sequence in context: A173740 A028275 A173118 * A147566 A204621 A146770

Adjacent sequences:  A147286 A147287 A147288 * A147290 A147291 A147292

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Nov 04 2008

EXTENSIONS

Edited by N. J. A. Sloane, Nov 07 2008

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 October 16 09:29 EDT 2019. Contains 328056 sequences. (Running on oeis4.)