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A127478 Triangle T(n,k) read by rows: matrix product A054523 * A054522. 4
1, 2, 1, 3, 0, 2, 4, 2, 0, 2, 5, 0, 0, 0, 4, 6, 3, 4, 0, 0, 2, 7, 0, 0, 0, 0, 0, 6, 8, 4, 0, 4, 0, 0, 0, 4, 9, 0, 6, 0, 0, 0, 0, 0, 6, 10, 5, 0, 0, 8, 0, 0, 0, 0, 4, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 12, 6, 8, 6, 0, 4, 0, 0, 0, 0, 0, 4, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 14, 7, 0, 0, 0, 0, 12, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

If the two matrices A054523 and A054522 are commuted, the matrix product becomes A127477.

LINKS

Table of n, a(n) for n=1..101.

FORMULA

T(n,k) = sum_{j=k..n} A054523(n,j) * A054522(j,k).

T(n,n) = A000010(n) (diagonal).

sum_{k=1..n} T(n,k) = A018804(n) (row sums).

EXAMPLE

First few rows of the triangle are:

.1;

.2, 1;

.3, 0, 2;

.4, 2, 0, 2;

.5, 0, 0, 0, 4;

.6, 3, 4, 0, 0, 2;

.7, 0, 0, 0, 0, 0, 6;

.8, 4, 0, 4, 0, 0, 0, 4;

....

MAPLE

A054522 := proc(n, k) if k = 1 then 1; elif n mod k = 0 then numtheory[phi](k) ; else 0 ; fi; end:

A054523 := proc(n, k) if k = n then 1; elif n mod k = 0 then numtheory[phi](n/k) ; else 0 ; fi; end:

A127478 := proc(n, k) add( A054523(n, j)*A054522(j, k), j=k..n) ; end: seq(seq( A127478(n, k), k=1..n), n=1..15) ;

CROSSREFS

Cf. A054522, A054523, A018804, A000010.

Sequence in context: A025649 A025642 A025643 * A127472 A194665 A004563

Adjacent sequences:  A127475 A127476 A127477 * A127479 A127480 A127481

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jan 15 2007

EXTENSIONS

Converted comments to formulas, extended - R. J. Mathar, Sep 11 2009

STATUS

approved

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Last modified November 16 17:25 EST 2019. Contains 329201 sequences. (Running on oeis4.)