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 A000397 Number of partitions into non-integral powers. (Formerly M4212 N1757) 2
 6, 32, 109, 288, 654, 1337, 2506, 4414, 7379, 11822, 18273, 27356, 39938, 56974, 79607, 109267, 147523, 196295, 257715, 334407, 429086, 545034, 685917, 855886, 1059360, 1301776, 1588321, 1925620, 2320544, 2780468, 3314007, 3930001, 4638319, 5449943, 6376505, 7430471, 8625369, 9976540, 11498855, 13210238, 15128487, 17272896, 19664754, 22326319, 25280987, 28554486, 32173404, 36166409, 40563607, 45397395, 50701682, 56512012, 62866699, 69805531, 77370606, 85607286, 94560129, 104280410, 114819255, 126229853, 138570284, 151899428, 166278945, 181775849, 198456941, 216394746, 235661505, 256338017, 278503009, 302242623, 327644632, 354799834, 383805368, 414759214, 447764499, 482931051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 5,1 COMMENTS a(n) counts the solutions to the inequality x_1^(1/2)+x_2^(1/2)+x_3^((1/2)<=n for any three distinct integers 1<=x_1= x2+1 then a := a+floor(x3-x2) ; fi; od: od: a ; end: for n from 5 do printf("%d, \n", A000397(n)) ; od: # R. J. Mathar, Sep 29 2009 MATHEMATICA A000397[n_] := Module[{a, x1, x2, x3}, a = 0; For[x1 = 1, x1 <= n^2, x1++, For[x2 = x1+1, x2 <= Floor[(n-x1^(1/2))^2], x2++, x3 = (n-x1^(1/2) - x2^(1/2))^2 ; If[Floor[x3] >= x2+1, a = a + Floor[x3-x2]]]]; a]; Reap[ For[n = 5, n <= 40, n++, Print[an = A000397[n]; Sow[an]]]][[2, 1]] (* Jean-François Alcover, Feb 08 2016, after R. J. Mathar *) CROSSREFS Sequence in context: A090382 A360839 A102359 * A200765 A239573 A130410 Adjacent sequences: A000394 A000395 A000396 * A000398 A000399 A000400 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS More terms from R. J. Mathar, Sep 29 2009 More terms from Sean A. Irvine, Nov 14 2010 STATUS approved

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Last modified June 19 06:35 EDT 2024. Contains 373492 sequences. (Running on oeis4.)