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A178086 Triangle T(n,m) = - phi(n+1) + phi(m+1) + phi(n-m+1), 0<=m<=n, where phi = A000010 is Euler's totient. 1
1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, -1, 0, -1, 1, 1, 3, 2, 2, 3, 1, 1, -3, 0, -2, 0, -3, 1, 1, 3, 0, 2, 2, 0, 3, 1, 1, -1, 2, -2, 2, -2, 2, -1, 1, 1, 3, 2, 4, 2, 2, 4, 2, 3, 1, 1, -5, -2, -4, 0, -6, 0, -4, -2, -5, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,17

COMMENTS

Row sums are 1, 2, 2, 4, 0, 12, -6, 12, 2, 24, -26,...

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,m) = T(n,n-m).

Sum_{m=0..n} T(n,m) = 2*A002088(n+1)-A002618(n+1). - R. J. Mathar, Feb 12 2013

EXAMPLE

1;

1, 1;

1, 0, 1;

1, 1, 1, 1;

1, -1, 0, -1, 1;

1, 3, 2, 2, 3, 1;

1, -3, 0, -2, 0, -3, 1;

1, 3, 0, 2, 2, 0, 3, 1;

1, -1, 2, -2, 2, -2, 2, -1, 1;

1, 3, 2, 4, 2, 2, 4, 2, 3, 1;

1, -5, -2, -4, 0, -6, 0, -4, -2, -5, 1;

MAPLE

A178086 := proc(n, m)

        -numtheory[phi](n+1)+numtheory[phi](m+1)+numtheory[phi](n-m+1)

end proc;

seq(seq(A178086(n, m), m=0..n), n=0..10) ; # R. J. Mathar, Feb 12 2013

MATHEMATICA

T[n_, m_, q_] := 1 - EulerPhi[n + q] + (EulerPhi[m + q] + EulerPhi[n - m + q]) - EulerPhi[q];

Table[Flatten[Table[Table[T[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10}]

PROG

(PARI) T(n, m)=-eulerphi(n+1)+eulerphi(m+1)+eulerphi(n-m+1) \\ Charles R Greathouse IV, Feb 12 2013

CROSSREFS

Sequence in context: A092106 A278885 A183049 * A281977 A240666 A052901

Adjacent sequences:  A178083 A178084 A178085 * A178087 A178088 A178089

KEYWORD

sign,tabl,easy

AUTHOR

Roger L. Bagula, May 19 2010

STATUS

approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)