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A210741 Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section. 3
1, 1, 3, 1, 5, 8, 1, 7, 19, 21, 1, 9, 34, 65, 55, 1, 11, 53, 141, 210, 144, 1, 13, 76, 257, 534, 654, 377, 1, 15, 103, 421, 1111, 1905, 1985, 987, 1, 17, 134, 641, 2041, 4447, 6512, 5911, 2584, 1, 19, 169, 925, 3440, 9038, 16837, 21557, 17345, 6765, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Rows end with even-indexed Fibonacci numbers
Row sums: A007070
Alternating row sums: signed powers of 2
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+1)*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
1...3
1...5...8
1...7...19...21
1...9...34...65...55
First three polynomials u(n,x): 1, 1+ 3x, 1 + 5x + 8x^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 + 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[%] (* A210741 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210742 *)
CROSSREFS
Sequence in context: A302191 A261712 A038738 * A208760 A340156 A340242
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 24 2012
STATUS
approved

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Last modified July 23 08:18 EDT 2024. Contains 374546 sequences. (Running on oeis4.)