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A208763 Triangle of coefficients of polynomials u(n,x) jointly generated with A208764; see the Formula section. 3
1, 1, 2, 1, 2, 6, 1, 2, 10, 14, 1, 2, 14, 26, 38, 1, 2, 18, 38, 90, 94, 1, 2, 22, 50, 158, 250, 246, 1, 2, 26, 62, 242, 470, 762, 622, 1, 2, 30, 74, 342, 754, 1614, 2138, 1606, 1, 2, 34, 86, 458, 1102, 2866, 4870, 6170, 4094, 1, 2, 38, 98, 590, 1514, 4582 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For a discussion and guide to related arrays, see A208510.

Subtriangle of the triangle given by (1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (0, 2, 1, -2, 0, 0, 0, 0, 0, 0, 0, ....) where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 19 2012

LINKS

Table of n, a(n) for n=1..62.

FORMULA

u(n,x)=u(n-1,x)+2x*v(n-1,x),

v(n,x)=2x*u(n-1,x)+x*v(n-1,x),

where u(1,x)=1, v(1,x)=1.

Contribution from Philippe Deléham, Mar 19 2012. (Start)

G.f. : (1-y*x+2*y*x^2-4*y^2*x^2)/(1-x-y*x+y*x^2-4*y^2*x^2).

T(n,k) = T(n-1,k) + T(n-1,k-1) - T(n-2,k-1) + 4*T(n-2,k-2), T(1,0) = 1, T(2,0) = 1, T(2,1) = 2, T(n,k) = 0 if k<0 or if k>=n. (End)

EXAMPLE

First five rows:

1

1...2

1...2...6

1...2...10...14

1...2...14...26...38

First five polynomials u(n,x):

1

1 + 2x

1 + 2x + 6x^2

1 + 2x + 10x^2 + 14x^3

1 + 2x + 14x^2 + 26x^3 + 38x^4

(1, 0, -1, 1, 0, 0, ...) DELTA (0, 2, 1, -2, 0, 0...) begins :

1

1, 0

1, 2, 0

1, 2, 6, 0

1, 2, 10, 14, 0

1, 2, 14, 26, 38, 0

1, 2, 18, 38, 90, 94, 0 . Philippe Deléham, Mar 19 2012

MATHEMATICA

u[1, x_] := 1; v[1, x_] := 1; z = 16;

u[n_, x_] := u[n - 1, x] + 2 x*v[n - 1, x];

v[n_, x_] := 2 x*u[n - 1, x] + x*v[n - 1, x];

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[%]    (* A208763 *)

Table[Expand[v[n, x]], {n, 1, z}]

cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];

TableForm[cv]

Flatten[%]    (* A208764 *)

CROSSREFS

Cf. A208764, A208510.

Sequence in context: A208757 A133643 A008305 * A249027 A307584 A266183

Adjacent sequences:  A208760 A208761 A208762 * A208764 A208765 A208766

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 02 2012

STATUS

approved

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Last modified October 16 02:52 EDT 2019. Contains 328038 sequences. (Running on oeis4.)