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A332311 Number of compositions (ordered partitions) of n into distinct parts where no part is a multiple of 5. 3
1, 1, 1, 3, 3, 4, 9, 11, 11, 19, 44, 31, 61, 87, 117, 144, 279, 311, 389, 541, 640, 1003, 1225, 2145, 2493, 3452, 3507, 5417, 6671, 8821, 11580, 17959, 21043, 26289, 34797, 41536, 59637, 72707, 85871, 110947, 172472, 175873, 249691, 327801, 418779, 512748 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Index entries for sequences related to compositions

EXAMPLE

a(6) = 9 because we have [6], [4, 2], [3, 2, 1], [3, 1, 2], [2, 4], [2, 3, 1], [2, 1, 3], [1, 3, 2] and [1, 2, 3].

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, 5), 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, 5], 1, n/i]}]]];

a[n_] := b[n, n, 0];

a /@ Range[0, 55] (* Jean-Fran├žois Alcover, Nov 17 2020, after Alois P. Heinz *)

CROSSREFS

Cf. A032020, A032021, A035959, A096938, A332309, A332310.

Sequence in context: A185395 A060372 A128036 * A332340 A045794 A065678

Adjacent sequences:  A332308 A332309 A332310 * A332312 A332313 A332314

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 09 2020

STATUS

approved

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Last modified April 15 04:04 EDT 2021. Contains 342974 sequences. (Running on oeis4.)