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A209698 Triangle of coefficients of polynomials v(n,x) jointly generated with A209697; see the Formula section. 3
1, 2, 2, 3, 4, 4, 4, 7, 10, 8, 5, 11, 20, 24, 16, 6, 16, 35, 54, 56, 32, 7, 22, 56, 104, 140, 128, 64, 8, 29, 84, 181, 294, 352, 288, 128, 9, 37, 120, 293, 552, 800, 864, 640, 256, 10, 46, 165, 449, 957, 1610, 2112, 2080, 1408, 512, 11, 56, 220, 659, 1562 (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*v(n-1,x),
v(n,x)=x*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...2
3...4....4
4...7....10...8
5...11...20...24...16
First three polynomials v(n,x): 1, 2 + 2x , 3 + 4x + 4x^2.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := x*u[n - 1, x] + x*v[n - 1, x];
v[n_, x_] := 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[%] (* A209697 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A209698 *)
CROSSREFS
Sequence in context: A208914 A049980 A359897 * A141525 A209764 A071475
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Mar 12 2012
STATUS
approved

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Last modified June 20 07:26 EDT 2024. Contains 373512 sequences. (Running on oeis4.)