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A000263 Number of partitions into non-integral powers.
(Formerly M2967 N1200)
2
3, 14, 39, 91, 173, 307, 502, 779, 1150, 1651, 2280, 3090, 4090, 5313, 6787, 8564, 10643, 13103, 15948, 19235, 23000, 27316, 32174, 37677, 43849, 50758, 58427, 66978, 76373, 86765, 98171, 110662, 124310, 139202, 155339, 172885 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
a(n) counts the solutions to the inequality x_1^(1/2)+x_2^(1/2)<=n for any two distinct integers 1<=x_1<x_2. - R. J. Mathar, Jul 03 2009
REFERENCES
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
B. K. Agarwala, F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
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. [Annotated scanned copy]
MAPLE
A000263 := proc(n) local a, x1, x2 ; a := 0 ; for x1 from 1 to n^2 do x2 := (n-x1^(1/2))^2 ; if floor(x2) >= x1+1 then a := a+floor(x2-x1) ; fi; od: a ; end: seq(A000263(n), n=3..80) ; # R. J. Mathar, Sep 29 2009
MATHEMATICA
A000263[n_] := Module[{a, x1, x2 }, a = 0; For[x1 = 1, x1 <= n^2, x1++, x2 = (n-x1^(1/2))^2; If[Floor[x2] >= x1+1, a = a+Floor[x2-x1]]]; a]; Table[ A000263[n], {n, 3, 80}] (* Jean-François Alcover, Feb 06 2016, after R. J. Mathar *)
CROSSREFS
Sequence in context: A162147 A319791 A027444 * A333293 A102590 A174517
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from R. J. Mathar, Sep 29 2009
STATUS
approved

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Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)