OFFSET
0,11
COMMENTS
Row sums = 2^floor(n/2).
T(n,0) = A053602(n-1) for n>0, T(n,1) = A079977(n-5) for n>4, T(2n+1,3) = A006367(n-1) for n>0, both bisections of column k=2 contain A010049. - Alois P. Heinz, Mar 21 2014
LINKS
Alois P. Heinz, Rows n = 0..140, flattened
FORMULA
G.f.: G(x,y) = ((1 + x)*(1 - x + x^2 + x*y - x^2*y))/(1 - x^2 - x^4 - x^2*y^2 + x^4*y^2). Satisfies G(x,y) = 1/(1 - x) - x + y*x + (x^2/(1 - x^2) - x^2 +y^2*x^2)*G(x,y).
EXAMPLE
1,
0, 1,
1, 0, 1,
1, 0, 0, 1,
2, 0, 1, 0, 1,
1, 1, 1, 0, 0, 1,
3, 0, 3, 0, 1, 0, 1,
2, 1, 1, 2, 1, 0, 0, 1,
5, 0, 5, 0, 4, 0, 1, 0, 1,
3, 2, 3, 2, 1, 3, 1, 0, 0, 1
There are eight palindromic compositions of 6: T(6,0)=3 because we have: 6, 3+3, 2+2+2. T(6,2)=3 because we have: 1+4+1, 2+1+1+2, 1+2+2+1. T(6,4)=1 because we have: 1+1+2+1+1. T(6,6)=1 because we have: 1+1+1+1+1+1.
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, expand(
add(b(n-j)*`if`(j=1, x^2, 1), j=1..n)))
end:
T:= n-> (p-> seq(coeff(p, x, i), i=0..n))
(add(b(i)*`if`(n-2*i=1, x, 1), i=0..n/2)):
seq(T(n), n=0..30); # Alois P. Heinz, Mar 21 2014
MATHEMATICA
nn=15; Table[Take[CoefficientList[Series[((1+x)*(1-x+x^2+x*y-x^2*y))/(1-x^2-x^4-x^2*y^2+x^4*y^2), {x, 0, nn}], {x, y}][[n]], n], {n, 1, nn}]//Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Mar 20 2014
STATUS
approved