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A185045 Triangle of coefficients of polynomials u(n,x) jointly generated with A208659; see the Formula section. 3
1, 1, 2, 1, 6, 4, 1, 10, 16, 8, 1, 14, 36, 40, 16, 1, 18, 64, 112, 96, 32, 1, 22, 100, 240, 320, 224, 64, 1, 26, 144, 440, 800, 864, 512, 128, 1, 30, 196, 728, 1680, 2464, 2240, 1152, 256, 1, 34, 256, 1120, 3136, 5824, 7168, 5632, 2560, 512, 1, 38, 324 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Alternating row sums:  1,-1,-1,-1,-1,-1,-1,-1,-1,...

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

LINKS

Table of n, a(n) for n=1..58.

FORMULA

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

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

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

T(n,k) = 2*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) - 2*T(n-2,k-1), T(1,0) = T(2,0) = T(3,0) = 1, T(2,1) = 2, T(3,1) = 6, T(3,2) = 4, T(n,k) = 0 if k<0 or if k>=n. - Philippe Deléham, Mar 19 2012

EXAMPLE

First five rows:

1

1...2

1...6...4

1...10...16...8

1...14...36...40...16

First five polynomials u(n,x):

1

1 + 2x

1 + 6x + 4x^2

1 + 10x + 16x^2 + 8x^3

1 + 14x + 36x^2 + 40x^3 + 16x^4

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_] := 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[%]    (* A185045 *)

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

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

TableForm[cv]

Flatten[%]    (* A208659 *)

CROSSREFS

Cf. A208659, A208510.

Sequence in context: A293409 A051482 A208923 * A208913 A208911 A208761

Adjacent sequences:  A185042 A185043 A185044 * A185046 A185047 A185048

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Mar 03 2012

STATUS

approved

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Last modified May 23 03:02 EDT 2019. Contains 323507 sequences. (Running on oeis4.)