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A209768 Triangle of coefficients of polynomials v(n,x) jointly generated with A209767; see the Formula section. 3
1, 2, 3, 3, 7, 7, 4, 14, 26, 17, 5, 24, 64, 83, 41, 6, 37, 130, 251, 250, 99, 7, 53, 233, 599, 899, 723, 239, 8, 72, 382, 1232, 2478, 3022, 2034, 577, 9, 94, 586, 2282, 5774, 9476, 9700, 5607, 1393, 10, 119, 854, 3908, 11952, 24734, 34152, 30063 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+(x+1)*v(n-1,x),
v(n,x)=2x*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
2...3
3...7....7
4...14...26...17
5...24...64...83...41
First three polynomials v(n,x): 1, 2 + 3x , 3 + 7x + 7x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + (x + 1)*v[n - 1, x];
v[n_, x_] := 2 x*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[%] (* A209767 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209768 *)
CROSSREFS
Sequence in context: A210558 A208920 A210234 * A209169 A222294 A181850
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 15 2012
STATUS
approved

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Last modified April 24 02:46 EDT 2024. Contains 371917 sequences. (Running on oeis4.)