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A210236 Triangle of coefficients of polynomials v(n,x) jointly generated with A210235; see the Formula section. 4
1, 3, 2, 6, 8, 3, 11, 22, 16, 4, 19, 52, 57, 28, 5, 32, 112, 166, 124, 45, 6, 53, 228, 428, 432, 241, 68, 7, 87, 446, 1018, 1300, 984, 432, 98, 8, 142, 848, 2285, 3540, 3397, 2036, 728, 136, 9, 231, 1578, 4912, 8964, 10443, 7962, 3914, 1168, 183, 10 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Row sums: powers of 3
Alternating row sums: 1,1,1,1,1,1,1,1,1,1,1,...
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)+(x+1)*v(n-1,x)+1
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3....2
6....8....3
11...22...16...4
19...52...57...28...5
First three polynomials v(n,x): 1, 3 + 2x , 6 + 8x + 3x^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] + (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[%] (* A210235 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210236 *)
CROSSREFS
Sequence in context: A273344 A370665 A127717 * A193998 A209171 A368150
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 20 2012
STATUS
approved

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Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)