A120475 - OEIS

%I #14 Dec 29 2023 12:06:31

%S -1,0,-2,1,1,-7,-7,14,14,14,-75,69,-164,-164,-164,823,823,823,823,

%T -5942,5004,5004,-23653,22715,-52310,-52310,144108,-173703,-173703,

%U -173703,-173703,2004606,2004606,2004606,2004606,2004606,-22153211,16934958,16934958,16934958,-148645183,119269113

%N a(n) = Sum_{m=1..n} A000045(m)*(A004001(m+1) - 2*A004001(m) + A004001(m-1)).

%p A000045 := proc(n) option remember ; combinat[fibonacci](n) ; end: A004001 := proc(n) option remember ; if n <= 0 then 0 ; elif n <= 2 then 1; else A004001(A004001(n-1))+A004001(n-A004001(n-1)) ; fi ; end: A120475 := proc(n) add( A000045(m)*(A004001(m+1)-2*A004001(m)+A004001(m-1)),m=1..n) ; end: seq(A120475(n),n=1..80) ; # _R. J. Mathar_, Sep 18 2007

%t Conway[0] = 0; Conway[1] = Conway[2] = 1; Conway[n_Integer?Positive] := Conway[n] = Conway[Conway[n - 1]] + Conway[n - Conway[n - 1]]; a[n_] := Fibonacci[n]*(Conway[n + 1] - 2*Conway[n] + Conway[n - 1]); Table[Sum[a[m], {m, 1, n}], {n, 1, 30}]

%Y Cf. A000045, A004001, A120474.

%K sign

%O 1,3

%A _Roger L. Bagula_, Jul 07 2006

%E Edited by _N. J. A. Sloane_, Aug 14 2006

%E More terms from _R. J. Mathar_, Sep 18 2007