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A210234 Triangle of coefficients of polynomials v(n,x) jointly generated with A210233; see the Formula section. 3
1, 2, 3, 3, 7, 7, 4, 14, 20, 15, 5, 22, 50, 53, 31, 6, 33, 92, 157, 134, 63, 7, 45, 161, 335, 455, 327, 127, 8, 60, 248, 666, 1112, 1248, 776, 255, 9, 76, 372, 1150, 2466, 3448, 3288, 1801, 511, 10, 95, 520, 1910, 4732, 8426, 10144, 8399, 4106, 1023, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
First and last terms of row n: n and -1+2^n
Alternating row sums: 3^(n-1)
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=x*u(n-1,x)+v(n-1,x)+1,
v(n,x)=(x+1)*u(n-1,x)+2x*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...20...15
5...22...50...53...31
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] + v[n - 1, x] + 1;
v[n_, x_] := (x + 1)*u[n - 1, x] + 2 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[%] (* A210233 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210234 *)
CROSSREFS
Sequence in context: A108346 A210558 A208920 * A209768 A209169 A222294
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved

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Last modified May 29 11:49 EDT 2024. Contains 372940 sequences. (Running on oeis4.)