A178536 - OEIS

%I #31 Jan 24 2021 13:28:10

%S 1,-2,-1,0,-1,1,-1,0,0,1,-1,0,-1,1,1,0,-1,0,-1,0,1,1,-1,0,0,1,0,0,-1,

%T -1,-1,0,1,1,1,0,-1,1,1,0,-1,-1,-1,0,0,1,-1,0,0,0,1,0,-1,0,1,0,1,1,-1,

%U 0,-1,1,0,0,1,-1,-1,0,1,-1,-1,0,-1,1,0,0,1,-1,-1,0,0,1,-1,0,1,1,1,0,-1,0,1,0

%N First column of A178535.

%C Except for the second term, a(n) seems to be equal to the Mobius function mu(n) = A008683(n) (verified for the first 53 terms).

%C a(n) = A008683(n) has now been verified for 3 <= n <= 800. - _R. J. Mathar_, Sep 14 2017

%H Antti Karttunen, <a href="/A178536/b178536.txt">Table of n, a(n) for n = 1..800</a> (prepared from the b-file of A008683 based on _R. J. Mathar_'s Sep 14 2017 comment)

%F a(n) = A178535(n,1).

%F a(n) = Sum_{k|n} A008683(n/k)*([k = 1] - [2|k]) (conjecture). - _Mats Granvik_, Jan 24 2021

%p A178536 := proc(n) A178535(n,1) ; end proc;

%p seq(A178536(n),n=1..80) ; # _R. J. Mathar_, Oct 28 2010

%t Clear[t, n, k, nn, a, A]; nn=92; a = Fibonacci[Range[nn] + 1]; t[n_, 1] = If[n >= 1, a[[n]], 0]; t[n_, k_] := t[n, k] = If[n >= k, Sum[t[n - i, k - 1], {i, 1, k - 1}] - Sum[t[n - i, k], {i, 1, k - 1}], 0]; MatrixForm[A = Table[Table[t[n, k], {k, 1, nn}], {n, 1, nn}]]; Inverse[A][[All, 1]] (* _Mats Granvik_, Sep 15 2017 *)

%Y Cf. A178535, A008683.

%Y Cf. also A181434, A181435.

%K sign

%O 1,2

%A _Mats Granvik_, May 29 2010

%E More terms from _R. J. Mathar_, Oct 28 2010