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A210191 Triangle of coefficients of polynomials u(n,x) jointly generated with A210192; see the Formula section. 3
1, 3, 5, 3, 7, 10, 3, 9, 21, 16, 3, 11, 36, 47, 22, 3, 13, 55, 104, 85, 28, 3, 15, 78, 195, 236, 135, 34, 3, 17, 105, 328, 535, 456, 197, 40, 3, 19, 136, 511, 1058, 1227, 788, 271, 46, 3, 21, 171, 752, 1897, 2820, 2471, 1256, 357, 52, 3, 23, 210, 1059, 3160 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Period of alternating row sums: (1,3,2,0)
For a discussion and guide to related arrays, see A208510.
LINKS
FORMULA
u(n,x)=u(n-1,x)+v(n-1,x)+1,
v(n,x)=2x*u(n-1,x)+x*v(n-1,x)+1,
where u(1,x)=1, v(1,x)=1.
EXAMPLE
First five rows:
1
3
5...3
7...10...3
9...21...16...3
First three polynomials u(n,x): 1, 3, 5 + 3x.
MATHEMATICA
u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + v[n - 1, x] + 1;
v[n_, x_] := 2 x*u[n - 1, x] + 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[%] (* A210191 *)
Table[Expand[v[n, x]], {n, 1, z}]
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%] (* A210192 *)
CROSSREFS
Sequence in context: A345280 A240499 A248511 * A110465 A354528 A328915
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Mar 18 2012
STATUS
approved

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)