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A208916 Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section. 3
1, 1, 3, 1, 3, 7, 1, 3, 11, 19, 1, 3, 15, 35, 47, 1, 3, 19, 51, 107, 123, 1, 3, 23, 67, 183, 323, 311, 1, 3, 27, 83, 275, 603, 939, 803, 1, 3, 31, 99, 383, 963, 1951, 2723, 2047, 1, 3, 35, 115, 507, 1403, 3411, 6147, 7723, 5259, 1, 3, 39, 131, 647, 1923, 5383 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+2x*v(n-1,x),
v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...3
1...3...7
1...3...11...19
1...3...15...35...47
First five polynomials v(n,x):
1
1 + 3x
1 + 3x + 7x^2
1 + 3x + 11x^2 + 19x^3
1 + 3x + 15x^2 + 35x^3 + 47x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];
v[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A208915 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208916 *)
CROSSREFS
Sequence in context: A208517 A336203 A209566 * A209766 A356207 A114972
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 03 2012
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)