The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A082375 Irregular triangle read by rows: row n begins with n and decreases by 2 until 0 or 1 is reached, for n >= 0. 3
 0, 1, 2, 0, 3, 1, 4, 2, 0, 5, 3, 1, 6, 4, 2, 0, 7, 5, 3, 1, 8, 6, 4, 2, 0, 9, 7, 5, 3, 1, 10, 8, 6, 4, 2, 0, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2, 0, 13, 11, 9, 7, 5, 3, 1, 14, 12, 10, 8, 6, 4, 2, 0, 15, 13, 11, 9, 7, 5, 3, 1, 16, 14, 12, 10, 8, 6, 4, 2, 0, 17, 15, 13, 11, 9, 7, 5, 3, 1, 18, 16, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS As a sequence, a(n) = A025644(n+1) for n <= 142. The length of row n is given by A008619(n) = 1 + floor(n/2). From Wolfdieter Lang, Feb 17 2020: (Start) This table T(n, m) can be used for the conversion identity 2*cos(Pi*k/N) = 2*sin((Pi/(2*N))*(N - 2*k)) = 2*sin((Pi/(2*N))*T(N-2, k-1)), here for N = n+2 >= 2, and k = m + 1 = 1, 2, ..., floor(N/2). 2*cos((Pi/N)*k) = R(k, rho(N)), where R is a monic Chebyshev polynomial from A127672 and rho(N) = 2*cos(Pi/N), gives part of the roots of the polynomial S(N-1, x), for k = 1, 2, ..., floor(N/2), with the Chebyshev S polynomials from A049310. 2*sin((Pi/(2*N))*q) = d^{(2*N)}_q/r, for q = 1, 2, ..., N, with the length ratio (q-th diagonal)/r, where r is the radius of the circle circumscribing a regular (2*N)-gon. The counting q starts with the diagonal d^{(2*N)}_1 = s(2*N) (in units of r), the side of the (2*N)-gon. The next diagonal is d^{(2*N)}_2 = rho(2*N)*s(2*N) (in units of r). For the instances N = 4 (n = 2) and 5 (n = 3) see the example section. (End) LINKS Harvey P. Dale, Table of n, a(n) for n = 0..1000 FORMULA T(n, m) = n - 2*m, m = 0, 1, ..., floor(n/2), n >= 0 (see the name and programs). - Wolfdieter Lang, Feb 17 2020 a(n) = A199474(n+1) - A122197(n+1). - Wesley Ivan Hurt, Jan 09 2022 EXAMPLE The irregular triangle T(n, m) begins: n\m  0 1 2 3 4 5 ... 0:   0 1:   1 2:   2 0 3:   3 1 4:   4 2 0 5:   5 3 1 6:   6 4 2 0 7:   7 5 3 1 8:   8 6 4 2 0 9:   9 7 5 3 1 10: 10 8 6 4 2 0 ... reformatted by Wolfdieter Lang, Feb 15 2020 From Wolfdieter Lang, Feb 17 2020: (Start) Conversion identity: N = n+2 = 4: k = m+1 = 1, 2*cos(Pi*1/4) = 2*sin(Pi*2/8) = sqrt(2); k=2, 2*cos(Pi*2/4) = 2*sin(Pi*0/8) = 0. N = 5:(n=3)  k=1 (m=0), 2*cos(Pi*1/5) = 2*sin(Pi*3/10) = (1 + sqrt(5))/2 = rho(5) = A001622; k=2: 2*cos(Pi*2/5) = 2*sin(Pi*1/10) = rho(5) - 1. (End) MATHEMATICA Flatten[Table[Range[n, 0, -2], {n, 0, 20}]] (* Harvey P. Dale, Apr 03 2019 *) PROG (PARI) a(n)=local(m); if(n<0, 0, m=sqrtint(1+4*n); m-1-(1+4*n-m^2)\2) CROSSREFS Cf. A008619, A122197, A199474. Sequence in context: A194549 A063277 A029178 * A025644 A022332 A215589 Adjacent sequences:  A082372 A082373 A082374 * A082376 A082377 A082378 KEYWORD nonn,tabf AUTHOR Michael Somos, Apr 09 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 20:21 EDT 2022. Contains 356039 sequences. (Running on oeis4.)