The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A209770 Triangle of coefficients of polynomials v(n,x) jointly generated with A209769; see the Formula section. 3
 1, 3, 1, 5, 4, 2, 9, 12, 10, 3, 15, 29, 33, 19, 5, 25, 64, 93, 77, 37, 8, 41, 132, 234, 251, 171, 69, 13, 67, 261, 548, 719, 629, 362, 127, 21, 109, 500, 1216, 1884, 2004, 1482, 742, 230, 34, 177, 936, 2592, 4628, 5784, 5196, 3342, 1482, 412, 55, 287 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Column 1: A001595 Row n ends with F(n), where F=A000045, the Fibonacci numbers. Row sums: 1,4,11,34,101,304,911,2734,... A060925 Alternating row sums: 1,2,3,4,5,6,7,.... A000027 For a discussion and guide to related arrays, see A208510. LINKS FORMULA u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x), v(n,x)=(x+1)*u(n-1,x)+v(n-1,x)+1, where u(1,x)=1, v(1,x)=1. EXAMPLE First five rows: 1 3....1 5....4....2 9....12...10...3 15...29...33...19...5 First three polynomials v(n,x): 1, 3 + x , 5 + 4x + 2x^2. MATHEMATICA u[1, x_] := 1; v[1, x_] := 1; z = 16; u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x]; v[n_, x_] := (x + 1)*u[n - 1, x] + 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[%] (* A209769 *) Table[Expand[v[n, x]], {n, 1, z}] cv = Table[CoefficientList[v[n, x], x], {n, 1, z}]; TableForm[cv] Flatten[%] (* A209770 *) CROSSREFS Cf. A209669, A208510. Sequence in context: A016574 A210560 A208922 * A210799 A068512 A011090 Adjacent sequences: A209767 A209768 A209769 * A209771 A209772 A209773 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 15 2012 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 January 27 09:05 EST 2023. Contains 359838 sequences. (Running on oeis4.)