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A210038
Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.
4
1, 3, 1, 7, 4, 1, 15, 12, 5, 1, 31, 32, 18, 6, 1, 63, 80, 56, 25, 7, 1, 127, 192, 160, 88, 33, 8, 1, 255, 448, 432, 280, 129, 42, 9, 1, 511, 1024, 1120, 832, 450, 180, 52, 10, 1, 1023, 2304, 2816, 2352, 1452, 681, 242, 63, 11, 1, 2047, 5120, 6912, 6400
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....1
7....4....1
15...12...5....1
31...32...18...6...1
First three polynomials v(n,x): 1, 3 + x , 7 + 4x + x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
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[%] (* A210037 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210038 *)
CROSSREFS
Sequence in context: A104709 A110814 A275599 * A319076 A286513 A193970
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 17 2012
STATUS
approved