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!)
A042984 Number of n-dimensional partitions of 6. 6
1, 11, 48, 140, 326, 657, 1197, 2024, 3231, 4927, 7238, 10308, 14300, 19397, 25803, 33744, 43469, 55251, 69388, 86204, 106050, 129305, 156377, 187704, 223755, 265031, 312066, 365428, 425720, 493581, 569687, 654752, 749529, 854811, 971432 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 190.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n) = A008780(n) - binomial(n, 4) - binomial(n, 3).

G.f.: (x^4 - 3*x^3 - 3*x^2 + 5*x + 1)/(x-1)^6. - Colin Barker, Jul 22 2012

a(n) = (n+1)*(n+4)*(n^3 + 40*n^2 + 61*n + 30)/120. - Robert Israel, Jul 06 2016

MAPLE

a:= n-> 1+10*n+27*binomial(n, 2)+28*binomial(n, 3)

              +11*binomial(n, 4)+binomial(n, 5):

seq(a(n), n=0..34);

MATHEMATICA

LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 11, 48, 140, 326, 657}, 40] (* Harvey P. Dale, Jan 27 2013 *)

CoefficientList[Series[(x^4 -3x^3 -3x^2 +5x +1)/(x-1)^6, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 27 2013 *)

PROG

(MAGMA) [1 + 10*n + 27*Binomial(n, 2) + 28*Binomial(n, 3) + 11*Binomial(n, 4) + Binomial(n, 5): n in [0..40]]; // Vincenzo Librandi, Oct 27 2013

(PARI) my(x='x+O('x^40)); Vec((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6) \\ G. C. Greubel, Feb 17 2019

(Sage) ((x^4-3*x^3-3*x^2+5*x+1)/(x-1)^6).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Feb 17 2019

(GAP) List([0..40], n->(n+1)*(n+4)*(n^3+40*n^2+61*n+30)/120); # Muniru A Asiru, Feb 17 2019

CROSSREFS

Cf. A007326, A007327, A008780.

Sequence in context: A230982 A024530 A117066 * A008780 A211058 A239460

Adjacent sequences:  A042981 A042982 A042983 * A042985 A042986 A042987

KEYWORD

nonn,easy

AUTHOR

Alford Arnold, Aug 15 1998

EXTENSIONS

More terms from Erich Friedman

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 August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)