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A210800 Triangle of coefficients of polynomials v(n,x) jointly generated with A210799; see the Formula section. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 03:34 EDT 2019. Contains 328211 sequences. (Running on oeis4.)