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A327710 Number of compositions of n into distinct parts such that the difference between any two parts is at least two. 3
1, 1, 1, 1, 3, 3, 5, 5, 7, 13, 15, 21, 29, 35, 43, 55, 87, 99, 137, 173, 235, 277, 363, 429, 545, 755, 895, 1135, 1443, 1827, 2285, 2837, 3463, 4285, 5199, 6309, 8237, 9755, 12091, 14743, 18351, 22251, 27833, 33125, 40819, 49045, 59691, 70869, 86033, 106163 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

All terms are odd.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k>=0} k! * A268187(n,k).

EXAMPLE

a(9) = 13: 135, 153, 315, 351, 513, 531, 36, 63, 27, 72, 18, 81, 9.

MAPLE

b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,

     `if`(n=0, p!, b(n, i-1, p)+b(n-i, min(n-i, i-2), p+1)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..50);

# second Maple program:

b:= proc(n, i) option remember; `if`(n=0, 1,

     `if`(i<1, 0, b(n, i-1)+b(n-i, min(n-i, i))))

    end:

a:= n-> add(k!*b(n-k^2, k), k=0..floor(sqrt(n))):

seq(a(n), n=0..50);

CROSSREFS

Cf. A003114, A032020, A268187, A268188, A328222.

Sequence in context: A237714 A245145 A092316 * A142456 A098508 A051593

Adjacent sequences:  A327707 A327708 A327709 * A327711 A327712 A327713

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 24 2020

STATUS

approved

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Last modified August 12 12:23 EDT 2020. Contains 336439 sequences. (Running on oeis4.)