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A208608 Triangle of coefficients of polynomials u(n,x) jointly generated with A208609; see the Formula section. 3
1, 1, 1, 1, 3, 2, 1, 5, 6, 3, 1, 7, 12, 12, 5, 1, 9, 20, 29, 23, 8, 1, 11, 30, 56, 64, 43, 13, 1, 13, 42, 95, 140, 136, 79, 21, 1, 15, 56, 148, 265, 332, 279, 143, 34, 1, 17, 72, 217, 455, 692, 751, 558, 256, 55, 1, 19, 90, 304, 728, 1295, 1708, 1641, 1093, 454 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
coefficient of x^(n-1)=Fibonacci(n)=A000045(n)
LINKS
FORMULA
u(n,x)=u(n-1,x)+x*v(n-1,x),
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
1...1
1...3...2
1...5...6....3
1...7...12...12...5
First five polynomials u(n,x):
1
1 + x
1 + 3x + 2x^2
1 + 5x + 6x^2 + 3x^3
1 + 7x + 12x^2 + 12x^3 + 5x^4
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + x*v[n - 1, x];
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[%] (* A208608 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A208609 *)
CROSSREFS
Cf. A208609.
Sequence in context: A132969 A132970 A192022 * A209577 A139377 A368607
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 29 2012
STATUS
approved

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Last modified March 28 16:34 EDT 2024. Contains 371254 sequences. (Running on oeis4.)