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A359452
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Number of vertices in the partite set of the n-Menger sponge graph that contains the corners.
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10
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1, 8, 208, 3968, 80128, 1599488, 32002048, 639991808, 12800032768, 255999868928, 5120000524288, 102399997902848, 2048000008388608, 40959999966445568, 819200000134217728, 16383999999463129088, 327680000002147483648, 6553599999991410065408, 131072000000034359738368
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OFFSET
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0,2
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COMMENTS
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This sequence and the sequence counting the non-corner vertices (A359453) alternate as to which is larger.
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LINKS
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FORMULA
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a(n) = (20^n + (-4)^n)/2.
O.g.f.: (1 - 8*x)/((1 - 20*x)*(1 + 4*x)).
E.g.f.: exp(8*x)*cosh(12*x). (End)
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EXAMPLE
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The level 1 Menger sponge graph can be formed by subdividing every edge of a cube graph. This produces a graph with 8 corner vertices and 12 non-corner vertices, so a(1) = 8.
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MATHEMATICA
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PROG
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(Python)
def A359452(n): return (10**n<<n-1)+(-(1<<(n<<1)-1) if n&1 else 1<<(n<<1)-1) if n else 1 # Chai Wah Wu, Feb 13 2023
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CROSSREFS
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Cf. A359453 (number of non-corner vertices).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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