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A035679
Number of partitions of n into parts 8k+1 and 8k+2 with at least one part of each type.
7
0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 7, 7, 10, 10, 13, 13, 16, 16, 22, 23, 30, 31, 38, 39, 46, 47, 58, 61, 75, 78, 93, 96, 111, 114, 134, 141, 167, 176, 204, 213, 242, 251, 286, 301, 346, 365, 416, 436, 489, 509, 570, 599, 676, 714, 802, 844, 937, 980, 1083, 1138, 1265
OFFSET
1,5
LINKS
MAPLE
b:= proc(n, i, t, s) option remember; `if`(n=0, t*s, `if`(i<1, 0,
b(n, i-1, t, s)+(h-> `if`(h in {1, 2}, add(b(n-i*j, i-1,
`if`(h=1, 1, t), `if`(h=2, 1, s)), j=1..n/i), 0))(irem(i, 8))))
end:
a:= n-> b(n$2, 0$2):
seq(a(n), n=1..75); # Alois P. Heinz, Sep 04 2020
MATHEMATICA
b[n_, i_, t_, s_] := b[n, i, t, s] = If[n == 0, t s, If[i < 1, 0, b[n, i - 1, t, s] + Function[h, If[h == 1 || h == 2, Sum[b[n - i j, i - 1, If[h == 1, 1, t], If[h == 2, 1, s]], {j, 1, n/i}], 0]][Mod[i, 8]]]];
a[n_] := b[n, n, 0, 0];
Array[a, 75] (* Jean-François Alcover, Oct 31 2020, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A005138 A357413 A318296 * A337587 A326439 A136537
KEYWORD
nonn
STATUS
approved