A210800 Triangle of coefficients of polynomials v(n,x) jointly generated with A210799; see the Formula section.

1, 1, 2, 5, 4, 3, 5, 14, 9, 5, 17, 28, 36, 19, 8, 17, 70, 88, 83, 38, 13, 53, 136, 251, 245, 181, 73, 21, 53, 298, 557, 746, 613, 379, 137, 34, 161, 568, 1376, 1930, 2030, 1439, 769, 252, 55, 161, 1162, 2888, 5026, 5818, 5139, 3221, 1524, 457, 89, 485

Offset

1,3

Comments

Row n starts a term of A048473 and ends with F(n+1), where F=A000045 (Fibonacci numbers).

Alternating row sums: 1,2,3,4,5,6,7,...

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

Links

Table of n, a(n) for n=1..56.

Formula

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

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

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

T(n,k) = T(n-1,k-1) + 3*T(n-2,k) + 2*T(n-2,k-1) + T(n-2,k-2) + a(k) with a(0) = 2, a(1) = 1, a(k) = 0 if k>1, T(1,0) = T(2,0) = 1, T(2,1) = 2 and T(n,k) = 0 if k<0 or if k >n. - Philippe Deléham, Mar 31 2012

Example

First five rows:
1
1....2
5....4....3
5....14...9....5
17...28...36...19...8
First three polynomials v(n,x): 1, 1 + 2x, 5 + 4x + 3x^2

Mathematica

u[1, x_] := 1; v[1, x_] := 1; z = 16;
u[n_, x_] := u[n - 1, x] + (x + j)*v[n - 1, x] + c;
d[x_] := h + x; e[x_] := p + x;
v[n_, x_] := d[x]*u[n - 1, x] + e[x]*v[n - 1, x] + f;
j = 1; c = 1; h = 2; p = -1; f = 0;
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[%]   (* A210799 *)
cv = Table[CoefficientList[v[n, x], x], {n, 1, z}];
TableForm[cv]
Flatten[%]   (* A210800 *)

Crossrefs

Cf. A210799, A208510.

Sequence in context: A272693 A184832 A111449 * A222235 A163332 A275105

Adjacent sequences: A210797 A210798 A210799 * A210801 A210802 A210803

Keyword

nonn,tabl

Author

Clark Kimberling, Mar 27 2012

Status

approved