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A210740 Triangle of coefficients of polynomials v(n,x) jointly generated with A210739; see the Formula section. 3
1, 2, 2, 2, 6, 5, 2, 7, 18, 13, 2, 7, 25, 53, 34, 2, 7, 26, 86, 154, 89, 2, 7, 26, 96, 286, 443, 233, 2, 7, 26, 97, 348, 926, 1264, 610, 2, 7, 26, 97, 361, 1234, 2935, 3582, 1597, 2, 7, 26, 97, 362, 1334, 4280, 9143, 10092, 4181, 2, 7, 26, 97, 362, 1350, 4875 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row n ends with odd-indexed Fibonacci numbers.
Limiting row: A001075.
Row sums: A003462.
Alternating row sums: 1,0,1,0,1,0,1,0,1,0,...
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x) = 2x*u(n-1,x) + x*v(n-1,x) + 1,
v(n,x) = (x+1)*u(n-1,x) + x*v(n-1,x) + 1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
2...2
2...6...5
2...7...18...13
2...7...25...53...34
First three polynomials v(n,x): 1, 2 + 2x, 2 + 6x + 5x^2
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*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[%] (* A210739 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210740 *)
CROSSREFS
Sequence in context: A211391 A309078 A241543 * A209820 A145890 A097091
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved

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Last modified April 21 04:54 EDT 2024. Contains 371850 sequences. (Running on oeis4.)