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 A229914 Number of pyramid polycubes of a given volume in dimension 3. 4
 1, 3, 7, 16, 33, 63, 117, 202, 344, 566, 908, 1419, 2206, 3334, 4988, 7378, 10778, 15535, 22281, 31547, 44405, 62011, 85939, 118281, 162136, 220494, 298531, 402163, 539181, 719301, 956287, 1265022, 1667973, 2190934, 2867470, 3739797, 4864163, 6303461, 8146863, 10499087, 13493267, 17293169, 22111954 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A pyramid polycube is obtained by gluing together horizontal plateaux (parallelepipeds of height 1) in such a way that (0,0,0) belongs to the first plateau and each cell of coordinate (0,b,c) belonging to the first plateau is such that b , c >= 0. If the cell with coordinates (a,b,c) belongs to the (a+1)-st plateau (a>0), then the cell with coordinates (a-1, b, c) belongs to the a-th plateau. LINKS Table of n, a(n) for n=1..43. C. Carré, N. Debroux, M. Deneufchatel, J.-Ph. Dubernard, C. Hillariet, J.-G. Luque, and O. Mallet, Enumeration of Polycubes and Dirichlet Convolutions, J. Int. Seq. 18 (2015) 15.11.4; also hal-00905889, version 1. FORMULA The generating function for the numbers of pyramids of height h and volumes v_1 , ... v_h is (n_1-n_2+1) *(n_2-n_3+1) *... *(n_{h-1}-n_h+1) *(x_1^{n_1} * ... x_h^{n_h}) / ((1-x_1^{n_1}) *(1-x_1^{n_1}*x_2^{n_2}) *... *(1-x_1^{n_1}*x_2^{n_2}*...x_h^{n_h})). This sequence is obtained with x_1 = ... = x_h = p by summing over n_1>=, ... >= n_h>=1 and then over h. CROSSREFS A001931 is an upper bound. Sequence in context: A318604 A084631 A219846 * A192968 A277968 A217942 Adjacent sequences: A229911 A229912 A229913 * A229915 A229916 A229917 KEYWORD nonn AUTHOR Matthieu Deneufchâtel, Oct 03 2013 STATUS approved

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Last modified September 23 03:16 EDT 2023. Contains 365532 sequences. (Running on oeis4.)