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%I #11 Jul 30 2015 05:34:25
%S 0,0,0,1,1,3,5,9,14,23,34,54,76,113,158,226,309,431,580,790,1049,1402,
%T 1838,2423,3140,4081,5242,6739,8574,10918,13780,17392,21795,27291,
%U 33969,42248,52258,64572,79429,97577,119388,145891,177630,215986,261789
%N Number of non-Fibonacci parts in all partitions of n.
%H Alois P. Heinz, <a href="/A144116/b144116.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A006128(n)-A144115(n).
%p b:= proc(n) option remember; true end: l:= [0, 1]: for k to 100 do b(l[1]):= false; l:= [l[2], l[1]+l[2]] od: aa:= proc(n, i) option remember; local g, h; if n=0 then [1, 0] elif i=0 or n<0 then [0, 0] else g:= aa(n, i-1); h:= aa(n-i, i); [g[1]+h[1], g[2]+h[2] +`if`(b(i), h[1], 0)] fi end: a:= n-> aa(n, n)[2]: seq(a(n), n=1..60); # _Alois P. Heinz_, Jul 28 2009
%t Clear[b]; b[_] = True; l = {0, 1}; For[k=1, k <= 100, k++, b[l[[1]]] = False; l = {l[[2]], l[[1]] + l[[2]]}]; aa[n_, i_] := aa[n, i] = Module[{g, h}, If[n==0, {1, 0}, If[i==0 || n<0, {0, 0}, g = aa[n, i-1]; h = aa[n-i, i]; {g[[1]] + h[[1]], g[[2]] + h[[2]] + If[b[i], h[[1]], 0]}] ]]; a[n_] := aa[n, n][[2]]; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Jul 30 2015, after _Alois P. Heinz_ *)
%Y Cf. A001690, A006128, A144115, A144117, A144118, A144119.
%K nonn
%O 1,6
%A _Omar E. Pol_, Sep 11 2008
%E More terms from _Alois P. Heinz_, Jul 28 2009
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