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A210187
Triangle of coefficients of polynomials u(n,x) jointly generated with A210188; see the Formula section.
3
1, 3, 6, 2, 10, 9, 2, 15, 25, 13, 2, 21, 55, 49, 17, 2, 28, 105, 140, 81, 21, 2, 36, 182, 336, 285, 121, 25, 2, 45, 294, 714, 825, 506, 169, 29, 2, 55, 450, 1386, 2079, 1716, 819, 225, 33, 2, 66, 660, 2508, 4719, 5005, 3185, 1240, 289, 37, 2, 78, 935, 4290
OFFSET
1,2
COMMENTS
Row sums: even-indexed Fibonacci numbers: 1,3,8,21,55,...
Column 1: triangular numbers: A000217
Alternating row sums: periodic with period (1,3,4,3,1,0)
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)=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
6....2
10...9....2
15...25...13...2
First three polynomials u(n,x): 1, 3, 6 + 2x.
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_] := 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[%] (* A210187 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210188 *)
CROSSREFS
Sequence in context: A360255 A353989 A354087 * A364365 A210189 A257506
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved