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A210550
Triangle of coefficients of polynomials v(n,x) jointly generated with A210549; see the Formula section.
3
1, 2, 2, 2, 6, 4, 2, 7, 16, 8, 2, 7, 23, 40, 16, 2, 7, 24, 71, 96, 32, 2, 7, 24, 81, 207, 224, 64, 2, 7, 24, 82, 266, 575, 512, 128, 2, 7, 24, 82, 279, 843, 1535, 1152, 256, 2, 7, 24, 82, 280, 939, 2572, 3967, 2560, 512, 2, 7, 24, 82, 280, 955, 3102, 7565, 9983
OFFSET
1,2
COMMENTS
Row sums: -1+odd-indexed Fibonacci numbers
For a discussion and guide to related arrays, see A208510.
FORMULA
u(n,x)=x*u(n-1,x)+x*v(n-1,x)+1,
v(n,x)=u(n-1,x)+2x*v(n-1,x)+1
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
2
2...2
2...6...4
2...7...16....8
2...7...28....40...16
First three polynomials v(n,x): 2, 2 + 2x , 2 + 6x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := u[n - 1, x] + 2 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[%] (* A210549 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210550 *)
CROSSREFS
Sequence in context: A158524 A054274 A053695 * A208659 A209752 A119918
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 22 2012
STATUS
approved