This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209148 Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section. 3
 1, 2, 1, 5, 5, 1, 11, 16, 7, 1, 23, 44, 30, 9, 1, 47, 112, 104, 48, 11, 1, 95, 272, 320, 200, 70, 13, 1, 191, 640, 912, 720, 340, 96, 15, 1, 383, 1472, 2464, 2352, 1400, 532, 126, 17, 1, 767, 3328, 6400, 7168, 5152, 2464, 784, 160, 19, 1, 1535, 7424 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,1,... For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x) = u(n-1,x) + (x+1)*v(n-1,x), v(n,x) = u(n-1,x) + (x+1)*v(n-1,x)+1, where u(1,x) = 1, v(1,x) = 1. T(n,k) = 3*T(n-1,k)+T(n-1,k-1)-2*T(n-2,k)-T(n-2,k-1), T(1,0)=T(2,1)=T(3,2)=1, T(2,0)=2, T(3,0)=T(3,1)=5, T(n,k)=0 if k<0 or if k>=n. - Philippe Deléham, Jan 17 2014 EXAMPLE First five rows:   1   2....1   5....5....1   11...16...7....1   23...44...30...9...1 First three polynomials v(n,x): 1, 2 + x, 5 + 5x + x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x]; v[n_, x_] := u[n - 1, x] + (x + 1)*v[n - 1, x] + 1; Table[Expand[u[n, x]], {n, 1, z/2}] Table[Expand[v[n, x]], {n, 1, z/2}] cu = Table[CoefficientList[u[n, x], x], {n, 1, z}]; TableForm[cu] Flatten[%]    (* A209148 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%]    (* A209149 *) CROSSREFS Cf. A209149, A208510. Sequence in context: A204111 A079502 A209164 * A126124 A123971 A060920 Adjacent sequences:  A209145 A209146 A209147 * A209149 A209150 A209151 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 07 2012 EXTENSIONS Example corrected by Philippe Deléham, Jan 17 2014 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 19 10:10 EST 2018. Contains 318246 sequences. (Running on oeis4.)