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A160182 Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. 2
1, 1, 1, 2, 1, 1, 3, 1, 1, 1, 5, 2, 1, 1, 1, 6, 2, 1, 1, 1, 1, 10, 4, 2, 1, 1, 1, 1, 11, 4, 2, 1, 1, 1, 1, 1, 16, 6, 3, 2, 1, 1, 1, 1, 1, 19, 7, 4, 2, 1, 1, 1, 1, 1, 1, 26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,4
COMMENTS
Inverse mobius transform (A051731) * the triangle shifts row terms to the right deleting the right border, getting triangle A160183: (1; 2,1; 3,1,1; 5,2,1,1;...).
LINKS
FORMULA
Triangle read by rows, 1 / ((-1)*A129184 * A051731 + I), I = Identity matrix. The operations shift the inverse Mobius transform (A051731) down, changing the signs to (-1), then add I = (1,1,1,...) as the right border.
EXAMPLE
First few rows of the triangle:
1;
1, 1;
2, 1, 1;
3, 1, 1, 1;
5, 2, 1, 1, 1;
6, 2, 1, 1, 1, 1;
10, 4, 2, 1, 1, 1, 1;
11, 4, 2, 1, 1, 1, 1, 1;
16, 6, 3, 2, 1, 1, 1, 1, 1;
19, 7, 4, 2, 1, 1, 1, 1, 1, 1;
26, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1;
...
MAPLE
A160182den := proc(n, k)
a := add( A129184(n, i)*A051731(i, k), i=1..n) ;
if n =k then
-a+1 ;
else
-a;
end if;
end proc:
N := 20 :
M := Matrix(N, N) :
for n from 1 to N do
for k from 1 to N do
M[n, k] := A160182den(n, k) ;
end do:
end do:
MatrixInverse(M) ; # R. J. Mathar, Aug 04 2015
CROSSREFS
Row sums = A068336. Left border = A003238.
Sequence in context: A124021 A109626 A182285 * A195825 A098824 A181651
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, May 03 2009
STATUS
approved

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)