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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026747 Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if n is even and 1<=k<=n/2, else T(n,k)=T(n-1,k-1)+T(n-1,k). 30
1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 11, 5, 1, 1, 7, 17, 16, 6, 1, 1, 9, 30, 44, 22, 7, 1, 1, 10, 39, 74, 66, 29, 8, 1, 1, 12, 58, 143, 184, 95, 37, 9, 1, 1, 13, 70, 201, 327, 279, 132, 46, 10, 1, 1, 15, 95, 329, 671, 790, 411, 178, 56, 11, 1, 1, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..67.

FORMULA

T(n, k) = number of paths from (0, 0) to (n-k, k) in the directed graph having vertices (i, j) and edges (i, j)-to-(i+1, j) and (i, j)-to-(i, j+1) for i, j >= 0 and edges (i, 2h+i)-to-(i+1, 2h+i+1) for i >= 0, h>=0.

EXAMPLE

1;

1,  1;

1,  3,  1;

1,  4,  4,  1;

1,  6, 11,  5,  1;

1,  7, 17, 16,  6,  1;

1,  9, 30, 44, 22,  7,  1;

MAPLE

A026747 := proc(n, k)

    if k=0 or k = n then

        1;

    elif type(n, 'even') and k <= n/2 then

        procname(n-1, k-1)+procname(n-2, k-1)+procname(n-1, k) ;

    else

        procname(n-1, k-1)+procname(n-1, k) ;

    end if ;

end proc: # R. J. Mathar, Jun 30 2013

CROSSREFS

Cf. A026754 (row sums).

Sequence in context: A026626 A136482 A026648 * A026374 A174032 A180979

Adjacent sequences:  A026744 A026745 A026746 * A026748 A026749 A026750

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling

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 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)