This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A160242 Triangle A(n,m) read by rows: a quarter of the Fourier coefficient [cos(m*t)] of the shifted Boubaker polynomial B_n(2*cos t)-2*cos(n*t). 0
 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Starting from the polynomials B_n(x) defined in A137276 and A135929, we insert x=2*cos(t), and define the Fourier coefficients A(n,m) by B_n(2*cos t)-2*cos(n*t) = 4*sum(m=0,..,n-2) A(n,m)*cos(m*t). A(n,m) is not an integer for n=0, so the table starts at n=1. Furthermore, A(n,m)=0 if n-m is odd, these regular zeros are skipped as usual, so effectively the first table entry appears at n=2. Simpler definition from R. J. Mathar, Apr 15 2010: a(n)=1 if n =0 or n in A002061, otherwise a(n)=2. So this is a kind of characteristic function of the central polygonal numbers A002061. LINKS A. Luzon and M. A. MorĂ³n, Recurrence relations for polynomial sequences via Riordan matrices, arXiv:0904.2672 [math.CO] EXAMPLE Using T^m =cos(m*t) as a notational shortcut, the expansions start ; B_1(2 cos t)-2*cos 1 t = 0 1 ; B_2(2 cos t)-2*cos 2 t = 1 0 2 ; B_3(2 cos t)-2*cos 3 t = 2*T 1 0 2 ; B_4(2 cos t)-2*cos 4 t = 1+2*T^2 0 2 0 2 ; B_5(2 cos t)-2*cos 5 t = 2*T+2*T^3 1 0 2 0 2 ; B_6(2 cos t)-2*cos 6 t = 1+2*T^2+2*T^4 0 2 0 2 0 2 ; B_7(2 cos t)-2*cos 7 t = 2*T+2*T^3+2*T^5 1 0 2 0 2 0 2 ; B_8(2 cos t)-2*cos 8 t = 1+2*T^2+2*T^4+2*T^6 0 2 0 2 0 2 0 2 ; B_9(2 cos t)-2*cos 9 t = 2*T+2*T^3+2*T^5+2*T^7 1 0 2 0 2 0 2 0 2 ; B_10(2 cos t)-2*cos 10 t = 1+2*T^2+2*T^4+2*T^6+2*T^8 0 2 0 2 0 2 0 2 0 2 ; B_11(2 cos t)-2*cos 11 t = 2*T^3+2*T^5+2*T^7+2*T^9+2*T CROSSREFS Sequence in context: A214860 A263649 A229904 * A043529 A201219 A254315 Adjacent sequences:  A160239 A160240 A160241 * A160243 A160244 A160245 KEYWORD nonn,tabl AUTHOR Haydar Rahmanov, May 05 2009 EXTENSIONS Definition clarified, publication title corrected, sequence extended by R. J. Mathar, Dec 07 2009 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.