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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A026811 Number of partitions of n in which the greatest part is 5. 12
0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70, 84, 101, 119, 141, 164, 192, 221, 255, 291, 333, 377, 427, 480, 540, 603, 674, 748, 831, 918, 1014, 1115, 1226, 1342, 1469, 1602, 1747, 1898, 2062, 2233, 2418, 2611, 2818, 3034, 3266, 3507, 3765 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Essentially same as A001401: five zeros followed by A001401.

Also number of partitions of n into exactly 5 parts.

REFERENCES

D. E. Knuth, The Art of Computer Programming, vol. 4, fascicle 3, Generating All Combinations and Partitions, Section 7.2.1.4., p.56, exercise 31.

LINKS

Washington Bomfim, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = round( ((n^4+10*(n^3+n^2)-75*n -45*n*(-1)^n)) / 2880 ). - Washington Bomfim, Jul 03 2012

G.f.: x^5/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)). [Joerg Arndt, Jul 04 2012]

a(n) = A008284(n,5). - Robert A. Russell, May 13 2018

MATHEMATICA

Table[Count[IntegerPartitions[n], {5, ___}], {n, 0, 55}] (* corrected by Harvey P. Dale, Oct 24 2011 *)

Table[Length[IntegerPartitions[n, {5}]], {n, 0, 55}] (* Eric Rowland, Mar 02 2017 *)

CoefficientList[Series[x^5/Product[1 - x^k, {k, 1, 5}], {x, 0, 65}], x] (* Robert A. Russell, May 13 2018 *)

Drop[LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1},

Append[Table[0, {14}], 1], 110], 9] (* Robert A. Russell, May 17 2018 *)

PROG

(PARI)

a(n)=round((n^4+10*(n^3+n^2)-75*n-45*(-1)^n*n)/2880);

for(n=0, 10000, print(n, " ", a(n))); /* b-file format */

/* Washington Bomfim, Jul 03 2012 */

(PARI) x='x+O('x^99); concat(vector(5), Vec(x^5/prod(k=1, 5, 1-x^k))) \\ Altug Alkan, May 17 2018

(GAP) List([0..70], n->NrPartitions(n, 5)); # Muniru A Asiru, May 17 2018

CROSSREFS

Cf. A026810, A026812, A026813, A026814, A026815, A026816, A002622 (partial sums), A008667 (first differences).

Sequence in context: A103232 A062684 A033485 * A001401 A008628 A038499

Adjacent sequences:  A026808 A026809 A026810 * A026812 A026813 A026814

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from Robert G. Wilson v, Jan 11 2002

a(0)=0 inserted by Joerg Arndt, Jul 04 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 22 22:58 EDT 2018. Contains 316518 sequences. (Running on oeis4.)