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A204842
Triangle by rows relating to A081696
1
1, 1, 2, 3, 4, 2, 9, 12, 6, 2, 29, 38, 20, 8, 2, 97, 126, 68, 30, 10, 2, 333, 430, 236, 110, 42, 12, 2, 1165, 1498, 832, 402, 166, 56, 14, 2, 4135, 5300, 2970, 1472, 640, 238, 72, 16, 2, 14845, 18980, 10710, 5410, 2440, 968, 328, 90, 18, 2
OFFSET
0,3
FORMULA
n-th row of the triangle is the top row of M^n, where M is the following infinite square production matrix:
1, 2, 0, 0, 0, 0,...
1, 1, 1, 0, 0, 0,...
1, 1, 1, 1, 0, 0,...
1, 1, 1, 1, 1, 0,...
1, 1, 1, 1, 1, 1,...
...
Conjecture: T(n,1) = 2*A109262(n). T(n,2)=2*A109263(n). - R. J. Mathar, Jul 21 2015
EXAMPLE
First few rows of the triangle =
1;
1, 2;
3, 4, 2;
9, 12, 6, 2;
29, 38, 20, 8, 2;
97, 126, 68, 30, 10, 2;
333, 430, 236, 110, 42, 12, 2;
1165, 1498, 832, 402, 166, 56, 14, 2;
4135, 5300, 2970, 1472, 640, 238, 72, 16, 2;
14845, 18980, 10710, 5410, 2440, 968, 328, 90, 18, 2;
...
Top row of M^3 = [9, 12, 6, 2, 0, 0, 0,...]
MAPLE
A204842T := proc(n, k)
if n =0 and k =1 then
2;
elif k <0 or k >n+1 then
0;
else
1;
end if ;
end proc:
A204842 := proc(n, k)
local A;
A := Matrix(n+1, n+1) ;
for row from 1 to n+1 do
for col from 1 to n+1 do
A[row, col] := A204842T(row-1, col-1) ;
end do:
end do:
Mn := LinearAlgebra[MatrixPower](A , n);
Mn[1, k+1] ;
end proc:
for n from 0 to 10 do
for k from 0 to n do
printf("%d ", A204842(n, k)) ;
end do:
printf("\n") ;
end do:
CROSSREFS
Cf. A081696 (first column and also row sums).
Sequence in context: A324911 A220335 A117009 * A103300 A305402 A213394
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jan 19 2012
STATUS
approved