login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A024793 Number of 9's in all partitions of n. 12
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 31, 43, 58, 80, 106, 142, 187, 246, 319, 416, 533, 685, 872, 1108, 1397, 1762, 2204, 2755, 3426, 4251, 5250, 6476, 7950, 9746, 11905, 14514, 17638, 21403, 25888, 31265, 37661, 45288, 54329, 65079, 77775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,11

COMMENTS

The sums of nine successive terms give A000070. - Omar E. Pol, Jul 12 2012

a(n) is also the difference between the sum of 9th largest and the sum of 10th largest elements in all partitions of n. - Omar E. Pol, Oct 25 2012

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = A181187(n,9) - A181187(n,10). - Omar E. Pol, Oct 25 2012

From Peter Bala, Dec 26 2013: (Start)

a(n+9) - a(n) = A000041(n).

a(n) + a(n+3) + a(n+6) = A024787(n).

O.g.f.: x^9/(1 - x^9) * product {k >= 1} 1/(1 - x^k) = x^9 + x^10 + 2*x^11 + 3*x^12 + ....

Asymptotic result: log(a(n)) ~ 2*sqrt(Pi^2/6)*sqrt(n) as n -> inf. (End)

a(n) ~ exp(Pi*sqrt(2*n/3)) / (18*Pi*sqrt(2*n)) * (1 - 109*Pi/(24*sqrt(6*n)) + (109/48 + 7993*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 05 2016

MAPLE

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

      if n=0 or i=1 then [1, 0]

    else g:= `if`(i>n, [0$2], b(n-i, i));

         b(n, i-1) +g +[0, `if`(i=9, g[1], 0)]

      fi

    end:

a:= n-> b(n, n)[2]:

seq(a(n), n=1..100);  # Alois P. Heinz, Oct 27 2012

MATHEMATICA

Table[ Count[ Flatten[ IntegerPartitions[n]], 9], {n, 1, 55} ]

(* second program: *)

b[n_, i_] := b[n, i] = Module[{g}, If[n == 0 || i == 1, {1, 0}, g = If[i > n, {0, 0}, b[n - i, i]]; b[n, i - 1] + g + {0, If[i == 9, g[[1]], 0]}]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 100}] (* Jean-Fran├žois Alcover, Oct 09 2015, after Alois P. Heinz *)

CROSSREFS

Cf.  A000041, A066633, A024786, A024787, A024788, A024789, A024790, A024791, A024792, A024794.

Sequence in context: A091582 A241727 A101977 * A116601 A218024 A236102

Adjacent sequences:  A024790 A024791 A024792 * A024794 A024795 A024796

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

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 April 25 03:57 EDT 2019. Contains 322449 sequences. (Running on oeis4.)