login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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 * A353296 A281977 A240666
KEYWORD
sign,tabl,easy
AUTHOR
Roger L. Bagula, May 19 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)