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A127069
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Number of lines in a Pauli graph of order n.
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0
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15, 45, 153, 561, 2145, 8385, 33153, 131841, 525825, 2100225, 8394753, 33566721, 134242305, 536920065, 2147581953, 8590131201, 34360131585, 137439739905, 549757386753, 2199026401281, 8796099313665, 35184384671745
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OFFSET
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2,1
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COMMENTS
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The number of vertices in a Pauli graph of order n is (4^n) - 1. Other invariants and a(n), are given in Table 5, p. 11, of Planat and Saniga.
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LINKS
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FORMULA
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G.f.: 3*x^2*(5 - 20*x + 16*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x)).
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n>4.
a(n) = (2 + 3*2^n + 4^n) / 2 for n>1.
(End)
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PROG
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(PARI) a(n) = my(t=2^(n-1), alfa=2^t-1, s=2*alfa); (t+1)*(s*t+alfa)/alfa; \\ Michel Marcus, May 28 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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