A144118 Number of non-Fibonacci parts in the last section of the set of partitions of n.

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

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