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A210037
Triangle of coefficients of polynomials u(n,x) jointly generated with A210038; see the Formula section.
3
1, 3, 7, 1, 15, 5, 1, 31, 17, 6, 1, 63, 49, 24, 7, 1, 127, 129, 80, 32, 8, 1, 255, 321, 240, 120, 41, 9, 1, 511, 769, 672, 400, 170, 51, 10, 1, 1023, 1793, 1792, 1232, 620, 231, 62, 11, 1, 2047, 4097, 4608, 3584, 2072, 912, 304, 74, 12, 1, 4095, 9217
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+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
7....1
15...5....1
31...17...6...1
First three polynomials u(n,x): 1, 3, 7 + x.
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: A124138 A135561 A196231 * A210197 A324715 A316665
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 17 2012
STATUS
approved