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A127477
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Triangle T(n,k) read by rows: matrix product A054522 * A054523.
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2
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1, 2, 1, 5, 0, 2, 6, 3, 0, 2, 17, 0, 0, 0, 4, 10, 5, 4, 0, 0, 2, 37, 0, 0, 0, 0, 0, 6, 22, 11, 0, 6, 0, 0, 0, 4, 41, 0, 14, 0, 0, 0, 0, 0, 6, 34, 17, 0, 0, 8, 0, 0, 0, 0, 4, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 30, 15, 12, 10, 0, 6, 0, 0, 0, 0, 0, 4, 145, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 74, 37, 0
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OFFSET
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1,2
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COMMENTS
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If the two matrices A054522 and A054523 are commuted, the matrix product becomes A127478.
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LINKS
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Table of n, a(n) for n=1..94.
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FORMULA
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T(n,k) = sum_{j=k..n} A054522(n,j) * A054523(j,k).
sum_{k=1..n} T(n,k) = A057660(n) (row sums).
T(n,n) = A000010(n) (diagonal).
T(n,1) = A029939(n).
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EXAMPLE
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First few rows of the triangle are:
1;
2, 1;
5, 0, 2;
6, 3, 0, 2;
17, 0, 0, 0, 4;
10, 5, 4, 0, 0, 2;
37, 0, 0, 0, 0, 0, 6;
22, 11, 0, 6, 0, 0, 0, 4;
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MAPLE
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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:
A127477 := proc(n, k) add( A054522(n, j)*A054523(j, k), j=k..n) ; end: seq(seq( A127477(n, k), k=1..n), n=1..15) ;
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CROSSREFS
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Cf. A054522, A054523, A057660, A000010, A029939.
Sequence in context: A322334 A198371 A352559 * A104505 A324185 A348175
Adjacent sequences: A127474 A127475 A127476 * A127478 A127479 A127480
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson, Jan 15 2007
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EXTENSIONS
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Converted comments to formulas, extended - R. J. Mathar, Sep 11 2009
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STATUS
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approved
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