This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A078807 Triangular array T given by T(n,k) = number of 01-words of length n having exactly k 1's, all runlengths odd and first letter 0. 4
 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2, 1, 1, 3, 3, 3, 2, 1, 0, 0, 1, 3, 4, 5, 4, 3, 1, 1, 4, 6, 7, 7, 5, 3, 1, 0, 0, 1, 4, 7, 10, 11, 10, 7, 4, 1, 1, 5, 10, 14, 17, 16, 13, 8, 4, 1, 0, 0, 1, 5, 11, 18, 24, 26, 24, 18, 11, 5, 1, 1, 6, 15, 25, 35, 40, 39, 32, 22, 12, 5, 1, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,12 COMMENTS Row sums: 1,1,2,3,5,8,13,..., the Fibonacci numbers (A000045). REFERENCES Clark Kimberling, Binary words with restricted repetitions and associated compositions of integers, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 194 (2009) 141-151. LINKS FORMULA T(n, k)=T(n-1, n-k-1)+T(n-3, n-k-3)+...+T(n-2m-1, n-k-2m-1), where m=[(n-1)/2] and (by definition) T(i, j)=0 if i<0 or j<0 or i=j. EXAMPLE T(6,2) counts the words 010001 and 000101. Top of triangle: 1 = T(1,0) 0 1 = T(2,0) T(2,1) 1 1 0 0 1 1 1 1 2 1 1 0 CROSSREFS Cf. A078808, A078821, A079487, A123245, A077419. Sequence in context: A137608 A191336 A277349 * A208249 A329985 A029422 Adjacent sequences:  A078804 A078805 A078806 * A078808 A078809 A078810 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Dec 07 2002 EXTENSIONS Row 0 removed to stick to the triangle format by Andrey Zabolotskiy, Sep 22 2017 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.

Last modified December 15 20:00 EST 2019. Contains 330000 sequences. (Running on oeis4.)