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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026568 Irregular triangular array T read by rows: T(i,0) = T(i,2i) = 1 for i >= 0; T(i,1) = T(i,2i-1) = [ (i+1)/2 ] for i >= 1; and for i >= 2 and 2 <=j <= i - 2, T(i,j) = T(i-1,j-2) + T(i-1,j-1) + T(i-1,j) if i + j is even, T(i,j) = T(i-1,j-2) + T(i-1,j) if i + j is odd. 26
1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 4, 5, 4, 2, 1, 1, 2, 7, 7, 13, 7, 7, 2, 1, 1, 3, 8, 16, 20, 27, 20, 16, 8, 3, 1, 1, 3, 12, 19, 44, 43, 67, 43, 44, 19, 12, 3, 1, 1, 4, 13, 34, 56, 106, 111, 153, 111, 106, 56, 34, 13, 4, 1, 1, 4, 18, 38, 103, 140, 273 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

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

LINKS

Clark Kimberling, Rows 0..100, flattened

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

EXAMPLE

First 5 rows:

  1

  1  1  1

  1  1  3  1  1

  1  2  4  5  4  2  1

  1  2  7  7 13  7  7  2  1

MATHEMATICA

z = 12; t[n_, 0] := 1; t[n_, 1] := Floor[(n + 1)/2]; t[n_, k_] := t[n, k] = Which[k == 2 n, 1, k == 2 n - 1, Floor[(n + 1)/2], EvenQ[n + k], t[n - 1, k - 2] + t[n - 1, k - 1] + t[n - 1, k], OddQ[n + k], t[n - 1, k - 2] + t[n - 1, k]]; u = Table[t[n, k], {n, 0, z}, {k, 0, 2 n}];

TableForm[u] (* A026568 array *)

Flatten[u]   (* A026568 sequence *)

PROG

(PARI) T(k, n)=if(n<0||n>2*k, 0, if(n==0||n==2*k, 1, if(k>0&&(n==1||n==2*k-1), (k+1)\2, T(k-1, n-2)+T(k-1, n)+if((k+n)%2==0, T(k-1, n-1))))) \\ Ralf Stephan

CROSSREFS

Cf. A026519, A026536, A026552, A026584, A027926.

Cf. T(n,n) is A026569.

Sequence in context: A136406 A242222 A247198 * A138361 A030408 A226048

Adjacent sequences:  A026565 A026566 A026567 * A026569 A026570 A026571

KEYWORD

nonn,tabf

AUTHOR

Clark Kimberling

EXTENSIONS

Updated by Clark Kimberling, Aug 28 2014

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.