Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A000327
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A000327 Number of partitions into non-integral powers.
(Formerly M3819 N1563)
+0
1
1, 5, 12, 23, 39, 62, 91, 127, 171, 228, 294, 370, 461, 561, 677, 811, 955, 1121, 1303, 1499, 1719, 1960, 2218, 2499, 2806, 3131, 3485, 3868, 4274, 4706, 5166, 5658, 6175, 6725, 7309, 7923, 8572, 9256, 9972, 10728, 11521, 12349, 13218, 14126, 15072 (list; graph; listen)
OFFSET

3,2

COMMENT

a(n) counts the solutions to the inequality x_1^(2/3)+x_2^(2/3)<=n for any two distinct integers 1<=x_1<x_2. - R. J. Mathar, Jul 03 2009

REFERENCES

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

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

B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.

LINKS

B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.

MAPLE

A000327 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to floor(n^(3/2)) do x2 := (n-x1^(2/3))^(3/2) ; if floor(x2) >= x1+1 then a := a+floor(x2-x1) ; fi; od: a ; end: seq(A000327(n), n=3..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009]

CROSSREFS

Adjacent sequences: A000324 A000325 A000326 this_sequence A000328 A000329 A000330

Sequence in context: A025740 A054307 A126573 this_sequence A130624 A066869 A023172

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 29 2009

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified November 8 07:45 EST 2009. Contains 166143 sequences.


AT&T Labs Research