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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 * A353296 A281977 A240666 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 July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)