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A130162 A051731 * A000837 as a diagonalized matrix. 2
1, 1, 1, 1, 0, 2, 1, 1, 0, 3, 1, 0, 0, 0, 6, 1, 1, 2, 0, 0, 7, 1, 0, 0, 0, 0, 0, 14, 1, 1, 0, 3, 0, 0, 0, 17, 1, 0, 2, 0, 0, 0, 0, 0, 27, 1, 1, 0, 0, 6, 0, 0, 0, 0, 34, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 55, 1, 1, 2, 3, 0, 7, 0, 0, 0, 0, 0, 63 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

Right border = A000837. Row sums = partition numbers A000041 starting (1, 2, 3, 5, 7,...).

LINKS

Table of n, a(n) for n=0..77.

FORMULA

A051731 * A000837 as a diagonalized matrix M, where M = T(n,k) = A000837(n) * 0^(n-k), 1<=k<=n; i.e. (1; 0,1; 0,0,2; 0,0,0,3; 0,0,0,0,6;...). A051731 = inverse Mobius transform.

EXAMPLE

First few rows of the triangle are:

1;

1, 1;

1, 0, 2;

1, 1, 0, 3;

1, 0, 0, 0, 6;

1, 1, 2, 0, 0, 7;

1, 0, 0, 0, 0, 0, 14;

1, 1, 0, 3, 0, 0, 0, 17;

...

MATHEMATICA

rows = 12; A000837[n_] := Sum[ MoebiusMu[n/d]*PartitionsP[d], {d, Divisors[n]}]; A000837diag = DiagonalMatrix[Array[A000837, rows]]; A051731 = Table[ If[Mod[n, k] == 0, 1, 0], {n, 1, rows}, {k, 1, rows}]; A130162 = A051731.A000837diag; Table[ A130162[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Oct 03 2013 *)

CROSSREFS

Cf. A051731, A000837, A000041.

Sequence in context: A152434 A143810 A128589 * A175595 A175417 A136481

Adjacent sequences:  A130159 A130160 A130161 * A130163 A130164 A130165

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 13 2007

EXTENSIONS

More terms from Jean-François Alcover, Oct 03 2013

STATUS

approved

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Last modified July 20 14:23 EDT 2019. Contains 325185 sequences. (Running on oeis4.)