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A000339 Number of partitions into non-integral powers.
(Formerly M3879 N1590)
2
1, 5, 18, 45, 100, 185, 323, 522, 804, 1180, 1687, 2322, 3139, 4146, 5377, 6859, 8645, 10733, 13203, 16058, 19356, 23132, 27460, 32330, 37846, 44031, 50954, 58637, 67203, 76613, 87021, 98443, 110951, 124616, 139526, 155681, 173246, 192243 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

a(n) counts the solutions to the inequality x_1^(1/2)+x_2^(1/2)<=n for any two 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=2..39.

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

A000339 := 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 then a := a+floor(x2-x1+1) ; fi; od: a ; end: for n from 2 to 80 do printf("%d, \n", A000339(n)) ; od: # R. J. Mathar, Sep 29 2009

MATHEMATICA

A000339[n_] := Module[{a, x1, x2}, a = 0; For[x1 = 1 , x1 <= n^2 , x1++, x2 = (n-x1^(1/2))^2; If[Floor[x2] >= x1, a = a+Floor[x2-x1+1]]]; a]; Reap[ For[n = 2, n <= 80, n++, Print[an = A000339[n]]; Sow[an]]][[2, 1]] (* Jean-Fran├žois Alcover, Feb 07 2016, after R. J. Mathar *)

CROSSREFS

Sequence in context: A101105 A037140 A007237 * A270944 A272457 A081435

Adjacent sequences:  A000336 A000337 A000338 * A000340 A000341 A000342

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 March 23 12:18 EDT 2017. Contains 283951 sequences.