A035679 Number of partitions of n into parts 8k+1 and 8k+2 with at least one part of each type.

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

Alois P. Heinz, Table of n, a(n) for n = 1..5000

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

Adjacent sequences: A035676 A035677 A035678 * A035680 A035681 A035682

Keyword

nonn

Author

Olivier Gérard

Status

approved