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 A014544 Numbers n such that a cube can be divided into n sub-cubes. 3
 1, 8, 15, 20, 22, 27, 29, 34, 36, 38, 39, 41, 43, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If m and n are in the sequence, so is m+n-1, since n-dissecting one cube in an m-dissection gives an (m+n-1)-dissection. 1, 8, 20, 38, 49, 51, 54 are in the sequence because of dissections corresponding to the equations 1^3=1^3, 2^3=8*1^3, 3^3=2^3+19*1^3, 4^3=3^3+37*1^3, 6^3=4*3^3+9*2^3+36*1^3, 6^3=5*3^3+5*2^3+41*1^3 and 8^3=6*4^3+2*3^3+4*2^3+42*1^3. Combining these facts gives the remaining terms shown and all numbers > 47. It may or may not have been shown that no other numbers occur - see Hickerson link. REFERENCES J.-P. Delahaye, Les inattendus mathematiques, pp. 93 Belin-Pour la science, Paris, 2004. Eves, Howard, A Survey of Geometry, Vol. 1. Allyn and Bacon, Inc., Boston, Mass. 1966, see p. 271. M. Gardner, Fractal Music, Hypercards and More: Mathematical Recreations from Scientific American Magazine. New York: W. H. Freeman, pp. 297-298, 1992. LINKS Dean Hickerson, Further comments on A014544, Nov 01 2007 and Nov 10 2007 Eric Weisstein's World of Mathematics, Cube Dissection Eric Weisstein's World of Mathematics, Hadwiger Problem Index entries for linear recurrences with constant coefficients, signature (2,-1). CROSSREFS Sequence in context: A161541 A247081 A133157 * A237610 A122754 A082867 Adjacent sequences:  A014541 A014542 A014543 * A014545 A014546 A014547 KEYWORD easy,nonn AUTHOR EXTENSIONS More terms from Jud McCranie, Mar 19 2001, who remarks that all integers > 47 are in the sequence. Edited by Dean Hickerson, Jan 05 2003 STATUS approved

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)