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A207634 Triangle of coefficients of polynomials v(n,x) jointly generated with A207633; see Formula section. 3
1, 2, 3, 3, 6, 6, 5, 13, 15, 12, 8, 26, 41, 36, 24, 13, 50, 95, 115, 84, 48, 21, 94, 210, 300, 302, 192, 96, 34, 173, 443, 740, 871, 760, 432, 192, 55, 314, 905, 1716, 2353, 2392, 1856, 960, 384, 89, 563, 1803, 3823, 5916, 6987, 6312, 4432, 2112, 768 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Column 1: Fibonacci numbers, A000045.
LINKS
FORMULA
u(n,x)=u(n-1,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
2...3
3...6....6
5...13...15...12
8...26...41...36...24
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x]
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 x*v[n - 1, x] + 1
Table[Factor[u[n, x]], {n, 1, z}]
Table[Factor[v[n, x]], {n, 1, z}]
cu = Table[CoefficientList[u[n, x], x], {n, 1, z}];
TableForm[cu]
Flatten[%] (* A207633 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A207634 *)
CROSSREFS
Cf. A207633.
Sequence in context: A321745 A212629 A127779 * A222862 A101437 A039856
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 24 2012
STATUS
approved

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Last modified February 24 00:49 EST 2024. Contains 370288 sequences. (Running on oeis4.)