This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A111940 Triangle P, read by rows, that satisfies [P^-1](n,k) = P(n+1,k+1) for n >= k >= 0, with P(k,k)=1 and P(k+1,1)=P(k+1,0) for k >= 0, where [P^-1] denotes the matrix inverse of P. 3
 1, 1, 1, -1, -1, 1, 0, 0, 1, 1, 0, 0, -1, -1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS FORMULA The g.f. of column k of matrix power P^m (ignoring leading zeros) is: cos(m*arccos(1-x^2/2)) + (-1)^k * sin(m*arccos(1-x^2/2)) * (1-x/2) / sqrt(1-x^2/4). EXAMPLE Triangle P begins:    1;    1,  1;   -1, -1,  1;    0,  0,  1,  1;    0,  0, -1, -1,  1;    0,  0,  0,  0,  1,  1;    0,  0,  0,  0, -1, -1,  1;    0,  0,  0,  0,  0,  0,  1,  1;    0,  0,  0,  0,  0,  0, -1, -1,  1; ... where P^-1 shifts columns left and up one place:    1;   -1,  1;    0,  1,  1;    0, -1, -1,  1;    0,  0,  0,  1,  1;    0,  0,  0, -1, -1,  1; ... PROG (PARI) {P(n, k, q=-1) = local(A=Mat(1), B); if(n

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 September 15 16:12 EDT 2019. Contains 327078 sequences. (Running on oeis4.)