This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A383338 #5 Apr 29 2025 13:40:57
%S A383338 1,2,1,2,4,1,2,8,8,1,2,12,26,14,1,2,16,56,76,20,1,2,20,98,244,150,28,
%T A383338 1,2,24,152,578,632,296,38,1,2,28,218,1138,1882,1680,558,48,1,2,32,
%U A383338 296,1984,4492,6424,4336,896,60,1,2,36,386,3176,9230,18908,21782,8688,1422,74,1
%N A383338 Square array read by antidiagonals, where the n-th row is the coordination sequence of a certain tiling with an n-dimensional analog of the X pentomino (or Greek cross), n >= 1.
%C A383338 The tile consists of an n-dimensional central hypercube with one hypercube attached to each of its 2*n (n-1)-dimensional facets. n-dimensional space can be tiled with this tile by placing the centers of the tiles at integer points (x_1, ..., x_n) for which Sum_{j=1..n} j*x_j is divisible by 2*n+1. (See problem B6 of the 2019 Putnam competition). Two tiles are considered to be neighbors if they share an (n-1)-dimensional facet.
%H A383338 Kiran S. Kedlaya, <a href="http://kskedlaya.org/putnam-archive/2019.pdf">The 80th William Lowell Putnam Mathematical Competition</a>, Dec 7 2019.
%H A383338 Kiran S. Kedlaya, <a href="http://kskedlaya.org/putnam-archive/2019s.pdf">Solutions to the 80th William Lowell Putnam Mathematical Competition</a>, Dec 7 2019.
%H A383338 Yusuke Nakamura, Ryotaro Sakamoto, Takafumi Mase, and Junichi Nakagawa, <a href="https://doi.org/10.1107/S2053273320016769">Coordination sequences of crystals are of quasi-polynomial type</a>, Acta Crystallographica A 77 (2021), 138-148.
%H A383338 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GreekCross.html">Greek Cross</a>.
%H A383338 <a href="/index/Con#coordseqs">Index entries for sequences related to coordination sequences</a>.
%F A383338 T(n,0) = 1.
%F A383338 T(n,1) = 2*A007980(n-1).
%F A383338 T(1,k) = A040000(k).
%F A383338 T(2,k) = A008574(k).
%F A383338 Empirically (do these formulas follow from the results of Nakamura et al.?):
%F A383338 T(3,k) = A005897(k).
%F A383338 T(4,k) = 10*k^3 - 7*k^2 + 13*k - 2 for k >= 1.
%F A383338 T(5,k) = (22/3)*k^4 - 4*k^3 + (50/3)*k^2 - 2*k + 2 for k >= 1.
%F A383338 T(6,k) = (32/5)*k^5 - 7*k^4 + 28*k^3 - 11*k^2 + (58/5)*k for k >= 1.
%F A383338 T(7,k) = (304/45)*k^6 - (284/15)*k^5 + (1237/18)*k^4 - 86*k^3 + (8777/90)*k^2 - (601/15)*k + 10 for k >= 1.
%e A383338 Array begins:
%e A383338 n\k| 0 1 2 3 4 5 6 7 8
%e A383338 ---+--------------------------------------------------
%e A383338 1 | 1 2 2 2 2 2 2 2 2
%e A383338 2 | 1 4 8 12 16 20 24 28 32
%e A383338 3 | 1 8 26 56 98 152 218 296 386
%e A383338 4 | 1 14 76 244 578 1138 1984 3176 4774
%e A383338 5 | 1 20 150 632 1882 4492 9230 17040 29042
%e A383338 6 | 1 28 296 1680 6424 18908 46416 99904 194768
%e A383338 7 | 1 38 558 4336 21782 80838 241730 616584 1393906
%e A383338 8 | 1 48 896 8688 52896 232000 803232 2332896 5923776
%Y A383338 Rows: A040000 (n=1), A008574 (n=2), A005897 (n=3; empirically).
%Y A383338 Cf. A007980.
%K A383338 nonn,tabl
%O A383338 1,2
%A A383338 _Pontus von Brömssen_, Apr 29 2025