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A210796 Triangle of coefficients of polynomials v(n,x) jointly generated with A210795; see the Formula section. 3
1, 1, 2, 3, 3, 3, 3, 7, 6, 5, 5, 10, 16, 12, 8, 5, 16, 26, 34, 23, 13, 7, 21, 47, 64, 70, 43, 21, 7, 29, 68, 123, 147, 140, 79, 34, 9, 36, 104, 200, 304, 324, 274, 143, 55, 9, 46, 140, 324, 538, 714, 690, 527, 256, 89, 11, 55, 195, 480, 932, 1366, 1616, 1431 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Row n starts with A109613(n) and ends with F(n+1), where F=A000045 (Fibonacci numbers).
Column 2: A114113
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x)+1,
v(n,x)=(x+2)*u(n-1,x)+(x-1)*v(n-1,x),
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...2
3...3....3
3...7....6....5
5...10...16...12...8
First three polynomials v(n,x): 1, 1 + 2x, 3 + 3x + 3x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 0; c = 1; h = 2; p = -1; f = 0;
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[%] (* A210795 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210796 *)
CROSSREFS
Sequence in context: A200924 A111913 A354142 * A305419 A075757 A096420
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 26 2012
STATUS
approved

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Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)