login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A238868 Number of partitions of n where the difference between consecutive parts is at most 8. 10
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 97, 129, 166, 217, 276, 356, 449, 572, 715, 900, 1117, 1393, 1717, 2123, 2601, 3193, 3889, 4744, 5748, 6970, 8404, 10135, 12165, 14600, 17448, 20845, 24813, 29522, 35009, 41491, 49031, 57900, 68195, 80258, 94234, 110553, 129421, 151382, 176724, 206132, 240002, 279195, 324255 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the number of partitions of n such that all parts, with the possible exception of the largest are repeated at most eight times (by taking conjugates).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

G.f.: 1 + sum(k>=1, q^k/(1-q^k) * prod(i=1..k-1, (1-q^(9*i))/(1-q^i) ) ).

a(n) = Sum_{k=0..8} A238353(n,k). - Alois P. Heinz, Mar 09 2014

MAPLE

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

      add(b(n-i*j, i-1), j=0..min(8, n/i))))

    end:

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

      add(b(n-i*j, i-1), j=1..n/i)))

    end:

a:= n-> add(g(n, k), k=0..n):

seq(a(n), n=0..60);  # Alois P. Heinz, Mar 09 2014

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[b[n - i*j, i-1], {j, 0, Min[8, n/i]}]]]; g[n_, i_] := g[n, i] = If[n == 0, 1, If[i<1, 0, Sum[b[n - i*j, i-1], {j, 1, n/i}]]]; a[n_] := Sum[g[n, k], {k, 0, n}]; Table[a[n], {n, 0, 60}] (* Jean-Fran├žois Alcover, Feb 18 2015, after Alois P. Heinz *)

PROG

(PARI) N=66;  q = 'q + O('q^N);

Vec( 1 + sum(k=1, N, q^k/(1-q^k) * prod(i=1, k-1, (1-q^(9*i))/(1-q^i) ) ) )

CROSSREFS

Sequences "number of partitions with max diff d": A000005 (d=0, for n>=1),  A034296 (d=1), A224956 (d=2), A238863 (d=3), A238864 (d=4), A238865 (d=5), A238866 (d=6), A238867 (d=7), this sequence, A238869 (d=9), A000041 (d --> infinity).

Sequence in context: A008639 A341914 A008633 * A035999 A036010 A328545

Adjacent sequences:  A238865 A238866 A238867 * A238869 A238870 A238871

KEYWORD

nonn

AUTHOR

Joerg Arndt, Mar 08 2014

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 June 19 03:38 EDT 2021. Contains 345125 sequences. (Running on oeis4.)