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A300008
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Inverse of the n-th 2 X 2 sandpile A300006(n).
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4
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2110, 2003, 2101, 1033, 1032, 1130, 1023, 1022, 2011, 1303, 1302, 2002, 333, 332, 331, 1031, 323, 322, 321, 1310, 1203, 1202, 1301, 233, 232, 231, 330, 223, 222, 221, 1210, 1103, 1201, 133, 132, 230, 123, 122, 1120, 1013, 3332, 3331, 1102, 3323, 3322, 3321, 131, 3313
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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As in A300006, a 2 X 2 sandpile [a,b;c,d] is encoded as 4-digit number concat(a,b,c,d), and a leading a = 0 is not displayed.
By definition, a(n) (+) A300006(n) = 2222, the neutral element, where the sandpile addition (+) is the regular addition followed by "toppling" of digits (i.e., matrix elements) larger than 3, as described in A300006.
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LINKS
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FORMULA
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PROG
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/*or*/ a(n, e=[2, 2; 2, 2])=for(i=1, #S2, spa(S2[i], S2[n])==e&&return(A300006[i])) \\ spa() and S2 are defined in A300006; A300006[i] is the decimal encoding of S2[i].
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CROSSREFS
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For links, references etc. see the main entry A300006.
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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