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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

Table of n, a(n) for n=3..38.

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-Fran├žois Alcover, Feb 06 2016, after R. J. Mathar *)

CROSSREFS

Sequence in context: A143941 A162147 A027444 * A102590 A174517 A034130

Adjacent sequences:  A000260 A000261 A000262 * A000264 A000265 A000266

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from R. J. Mathar, Sep 29 2009

STATUS

approved

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Last modified June 25 00:41 EDT 2017. Contains 288708 sequences.