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 A144118 Number of non-Fibonacci parts in the last section of the set of partitions of n. 5
 0, 0, 0, 1, 0, 2, 2, 4, 5, 9, 11, 20, 22, 37, 45, 68, 83, 122, 149, 210, 259, 353, 436, 585, 717, 941, 1161, 1497, 1835, 2344, 2862, 3612, 4403, 5496, 6678, 8279, 10010, 12314, 14857, 18148, 21811, 26503, 31739, 38356, 45803, 55066, 65553, 78488, 93129 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS First differences of A144116. LINKS Table of n, a(n) for n=1..49. FORMULA a(n) = A138137(n)-A144117(n) = A144116(n)-A144116(n-1). MAPLE 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 MATHEMATICA 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 *) CROSSREFS Cf. A001690, A135010, A138121, A138137, A144115, A144116, A144117, A144121. Sequence in context: A240206 A229816 A099574 * A187069 A038000 A089935 Adjacent sequences: A144115 A144116 A144117 * A144119 A144120 A144121 KEYWORD nonn AUTHOR Omar E. Pol, Sep 11 2008 EXTENSIONS More terms from Alois P. Heinz, Jul 28 2009 STATUS approved

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Last modified March 1 16:12 EST 2024. Contains 370442 sequences. (Running on oeis4.)