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A332310
Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 4.
2
1, 1, 1, 3, 2, 3, 9, 5, 12, 17, 23, 43, 50, 55, 67, 111, 144, 273, 291, 377, 410, 689, 827, 961, 1860, 1663, 2647, 3573, 4610, 4683, 6753, 8465, 11232, 16835, 19985, 24073, 29258, 40411, 51367, 58431, 72084, 99807, 119409, 176387, 199922, 250841, 290123
OFFSET
0,4
EXAMPLE
a(7) = 5 because we have [7], [6, 1], [5, 2], [2, 5] and [1, 6].
MAPLE
b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0,
p!, add(b(n-i*j, i-1, p+j), j=0..min(irem(i, 4), 1, n/i))))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..55); # Alois P. Heinz, Feb 09 2020
MATHEMATICA
b[n_, i_, p_] := b[n, i, p] = If[i(i+1)/2 < n, 0, If[n == 0, p!, Sum[b[n - i j, i - 1, p + j], {j, 0, Min[Mod[i, 4], 1, n/i]}]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 55] (* Jean-François Alcover, Nov 17 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 09 2020
STATUS
approved