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A000711 Number of partitions of n, with three kinds of 1,2,3 and 4 and two kinds of 5,6,7,...
(Formerly M2787 N1122)
8
1, 3, 9, 22, 51, 107, 217, 416, 775, 1393, 2446, 4185, 7028, 11569, 18749, 29908, 47083, 73157, 112396, 170783, 256972, 383003, 565961, 829410, 1206282, 1741592, 2497425, 3557957, 5037936, 7091711, 9927583, 13823626, 19151731, 26404879, 36236988, 49509149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A000712 and A001400. - Vaclav Kotesovec, Aug 18 2015

REFERENCES

H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

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

M. A. Harrison, On the number of classes of binary matrices, IEEE Transactions on Computers, C-22.12 (1973), 1048-1052. (Annotated scanned copy)

N. J. A. Sloane, Transforms

FORMULA

EULER transform of 3, 3, 3, 3, 2, 2, 2, 2...

G.f.: 1/[(1-x)(1-x^2)(1-x^3)(1-x^4)product((1-x^k)^2, k=1..infinity)].

a(n) ~ exp(2*Pi*sqrt(n/3)) * 3^(1/4) * n^(3/4) / (32*Pi^4). - Vaclav Kotesovec, Aug 18 2015

EXAMPLE

a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".

MAPLE

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:= etr(n-> `if`(n<5, 3, 2)): seq(a(n), n=0..40); # Alois P. Heinz, Sep 08 2008

MATHEMATICA

nn=31; CoefficientList[Series[1/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/Product[(1-x^i)^2, {i, 1, nn}], {x, 0, nn}], x] (* Geoffrey Critzer, Sep 28 2013 *)

CROSSREFS

Sequence in context: A034505 A143099 A160462 * A278668 A160526 A121589

Adjacent sequences:  A000708 A000709 A000710 * A000712 A000713 A000714

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended with formula from Christian G. Bower, Apr 15 1998.

Edited by Emeric Deutsch, Mar 22 2005

STATUS

approved

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Last modified October 22 04:25 EDT 2019. Contains 328315 sequences. (Running on oeis4.)