This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A117418 Triangle T, read by rows, such that column 2k+1 of T equals column k of T^2 and column 2k of T equals column k of T*R: [T^2](n+k,k) = T(n+2k+1,2k+1) and [T*R](n+k,k) = T(n+2k,2k) for n>=0, k>=0, where R = SHIFT_RIGHT(T). 8
 1, 1, 1, 1, 2, 1, 1, 4, 3, 1, 1, 9, 8, 4, 1, 1, 23, 22, 14, 5, 1, 1, 66, 65, 50, 20, 6, 1, 1, 209, 208, 191, 79, 28, 7, 1, 1, 724, 723, 780, 322, 126, 37, 8, 1, 1, 2722, 2721, 3415, 1385, 572, 180, 48, 9, 1, 1, 11054, 11053, 15924, 6293, 2692, 871, 264, 58, 10, 1, 1, 48221 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Here SHIFT_RIGHT(T) shifts the columns of T one place to the right and fills column 0 with [1,0,0,0,...]. LINKS FORMULA T(n,2k+1) = Sum_{j=0..n-2k-1} T(n-k-1,k+j)*T(k+j,k) for n>2k and T(n,2k) = Sum_{j=0..n-2k} T(n-k,k+j)*T(k-1+j,k-1) for n>=2k, with T(n,n)=T(n,0)=1. EXAMPLE Triangle T begins: 1; 1, 1; 1, 2, 1; 1, 4, 3, 1; 1, 9, 8, 4, 1; 1, 23, 22, 14, 5, 1; 1, 66, 65, 50, 20, 6, 1; 1, 209, 208, 191, 79, 28, 7, 1; 1, 724, 723, 780, 322, 126, 37, 8, 1; 1, 2722, 2721, 3415, 1385, 572, 180, 48, 9, 1; 1, 11054, 11053, 15924, 6293, 2692, 871, 264, 58, 10, 1; ... The matrix square T^2 = A117427: 1; 2, 1; 4, 4, 1; 9, 14, 6, 1; 23, 50, 28, 8, 1; 66, 191, 126, 48, 10, 1; 209, 780, 572, 264, 70, 12, 1; ... where column k of T^2 equals column 2k+1 of T. Let matrix R = SHIFT_RIGHT(T): 1; 0, 1; 0, 1, 1; 0, 1, 2, 1; 0, 1, 4, 3, 1; 0, 1, 9, 8, 4, 1; 0, 1, 23, 22, 14, 5, 1; ... then matrix product T*R = A117425: 1; 1, 1; 1, 3, 1; 1, 8, 5, 1; 1, 22, 20, 7, 1; 1, 65, 79, 37, 9, 1; 1, 208, 322, 180, 58, 11, 1; ... where column k of T*R equals column 2k of T. PROG (PARI) {T(n, k)=if(n

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .