login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339165 Number of compositions (ordered partitions) of n into distinct parts, the least being 4. 8
0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 8, 8, 14, 14, 20, 20, 26, 50, 56, 80, 110, 134, 164, 212, 242, 410, 464, 632, 806, 1118, 1292, 1724, 2042, 2594, 3752, 4448, 5726, 7382, 9524, 12020, 15122, 18602, 23264, 28424, 39830, 46670, 60476, 74780 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

Table of n, a(n) for n=0..52.

Index entries for sequences related to compositions

FORMULA

G.f.: Sum_{k>=1} k! * x^(k*(k + 7)/2) / Product_{j=1..k-1} (1 - x^j).

EXAMPLE

a(15) = 8 because we have [11, 4], [6, 5, 4], [6, 4, 5], [5, 6, 4], [5, 4, 6], [4, 11], [4, 6, 5] and [4, 5, 6].

MAPLE

b:= proc(n, i, p) option remember;

      `if`(n=0, p!, `if`((i-4)*(i+5)/2<n, 0,

       add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))

    end:

a:= n-> `if`(n<4, 0, b(n-4$2, 1)):

seq(a(n), n=0..55);  # Alois P. Heinz, Nov 25 2020

MATHEMATICA

nmax = 52; CoefficientList[Series[Sum[k! x^(k (k + 7)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A026797, A026825, A339102, A339162, A339163, A339164, A339166.

Sequence in context: A172009 A299150 A202448 * A129381 A319991 A323275

Adjacent sequences:  A339162 A339163 A339164 * A339166 A339167 A339168

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Nov 25 2020

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 01:45 EST 2022. Contains 350473 sequences. (Running on oeis4.)