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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026386 Triangular array T read by rows: T(n,0) = T(n,n) = 1 for all n >= 0; T(n,k) = T(n-1,k-1) + T(n-1,k) for even n and k = 1..n-1; T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-2,k-1) for odd n and k = 1 ..n-1. 17
1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 5, 8, 5, 1, 1, 7, 17, 17, 7, 1, 1, 8, 24, 34, 24, 8, 1, 1, 10, 39, 75, 75, 39, 10, 1, 1, 11, 49, 114, 150, 114, 49, 11, 1, 1, 13, 70, 202, 339, 339, 202, 70, 13, 1, 1, 14, 83, 272, 541, 678, 541, 272, 83, 14, 1, 1, 16 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

T(n, k) = number of integer strings s(0)..s(n) such that s(0) = 0, s(n) = n - 2k, where, for u = 1..n, s(i) is odd if i is odd and |s(i)-s(i-1)| <=1.

LINKS

Clark Kimberling, Rows n = 0..100, flattened

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

Rows n=0 through n=7:

  1

  1 ... 1

  1 ... 2 ... 1

  1 ... 4 ... 4 ... 1

  1 ... 5 ... 8 ... 5 ... 1

  1 ... 7 ... 17 .. 17 .. 7 ... 1

  1 ... 8 ... 24 .. 34 .. 24 .. 8 ... 1

  1 ... 10 .. 39 .. 75 .. 75 .. 39 .. 10 ... 1

MAPLE

A026386 := proc(n, k)

    option remember;

    if k=0 or k = n then

        1;

    elif k <0 or k > n then

        0 ;

    elif type(n, 'even') then

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

    else

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

    end if;

end proc: # R. J. Mathar, Feb 10 2015

MATHEMATICA

z = 12; t[n_, 0] := 1; t[n_, n_] := 1; t[n_, k_] := t[n, k] =

Which[EvenQ[n], t[n - 1, k - 1] + t[n - 1, k], OddQ[n], t[n - 1, k - 1] +

t[n - 1, k] + t[n - 2, k - 1]]; u = Table[t[n, k], {n, 0, z}, {k, 0, n}];

TableForm[u] (* A026386 array *)

Flatten[u]   (* A026386 sequence *)

CROSSREFS

Cf. A007318.

Sequence in context: A156609 A026637 A026659 * A147532 A283796 A156580

Adjacent sequences:  A026383 A026384 A026385 * A026387 A026388 A026389

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Updated by Clark Kimberling, Aug 28 2014

Offset corrected by R. J. Mathar, Feb 10 2015

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 February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)