A144116 Number of non-Fibonacci parts in all partitions of n.

0, 0, 0, 1, 1, 3, 5, 9, 14, 23, 34, 54, 76, 113, 158, 226, 309, 431, 580, 790, 1049, 1402, 1838, 2423, 3140, 4081, 5242, 6739, 8574, 10918, 13780, 17392, 21795, 27291, 33969, 42248, 52258, 64572, 79429, 97577, 119388, 145891, 177630, 215986, 261789

Offset

1,6

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

a(n) = A006128(n)-A144115(n).

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]: 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]]}]; 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 *)

Crossrefs

Cf. A001690, A006128, A144115, A144117, A144118, A144119.

Sequence in context: A320598 A227567 A120452 * A294424 A061556 A053993

Adjacent sequences: A144113 A144114 A144115 * A144117 A144118 A144119

Keyword

nonn

Author

Omar E. Pol, Sep 11 2008

Extensions

More terms from Alois P. Heinz, Jul 28 2009

Status

approved