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%I A144118 #10 Dec 05 2016 09:03:20
%S A144118 0,0,0,1,0,2,2,4,5,9,11,20,22,37,45,68,83,122,149,210,259,353,436,585,
%T A144118 717,941,1161,1497,1835,2344,2862,3612,4403,5496,6678,8279,10010,
%U A144118 12314,14857,18148,21811,26503,31739,38356,45803,55066,65553,78488,93129
%N A144118 Number of non-Fibonacci parts in the last section of the set of partitions of n.
%C A144118 First differences of A144116.
%F A144118 a(n) = A138137(n)-A144117(n) = A144116(n)-A144116(n-1).
%p A144118 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] -aa(n-1, n-1)[2]: seq(a(n), n=1..60); # _Alois P. Heinz_, Jul 28 2009
%t A144118 Clear[b]; b[_] = True; l = {0, 1}; For[k = 1, k <= 100, k++, b[l[[1]]] = False; l = {l[[2]], l[[1]] + l[[2]]}]; a[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]] - aa[n-1, n-1][[2]]; Table[a[n], {n, 1, 60}] (* _Jean-François Alcover_, Dec 05 2016 after _Alois P. Heinz_ *)
%Y A144118 Cf. A001690, A135010, A138121, A138137, A144115, A144116, A144117, A144121.
%K A144118 nonn
%O A144118 1,6
%A A144118 _Omar E. Pol_, Sep 11 2008
%E A144118 More terms from _Alois P. Heinz_, Jul 28 2009