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A188377
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a(n) = n^3 - 4n^2 + 6n - 2.
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21
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7, 22, 53, 106, 187, 302, 457, 658, 911, 1222, 1597, 2042, 2563, 3166, 3857, 4642, 5527, 6518, 7621, 8842, 10187, 11662, 13273, 15026, 16927, 18982, 21197, 23578, 26131, 28862, 31777, 34882, 38183, 41686, 45397, 49322, 53467, 57838, 62441, 67282, 72367
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OFFSET
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3,1
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COMMENTS
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Number of nilpotent elements in the identity difference partial one - one transformation semigroup, denoted by N(IDI_n). For n=3, #N(IDI_n) = 7.
a(n+1) is also the Moore lower bound on the order of an (n,7)-cage. - Jason Kimberley, Oct 20 2011
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LINKS
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FORMULA
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a(n+1) = (n+1)^3 - 4*(n+1)^2 + 6*(n+1) - 2
= (n-1)^3 + 2*(n-1)^2 + 2*(n-1) + 2
= 1222 read in base n-1.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: x^3*(7 - 6*x + 7*x^2 - 2*x^3)/(1-x)^4. (End)
E.g.f.: 2 - x - x^2 + exp(x)*(x^3 - x^2 + 3*x - 2). - Stefano Spezia, Apr 09 2022
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MATHEMATICA
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LinearRecurrence[{4, -6, 4, -1}, {7, 22, 53, 106}, 50] (* Harvey P. Dale, May 29 2019 *)
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PROG
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(Magma) [SequenceToInteger([2^^3, 1], n-2):n in [5..50]]; // Jason Kimberley, Oct 20 2011
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CROSSREFS
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Moore lower bound on the order of a (k,g) cage: A198300 (square); rows: A000027 (k=2), A027383 (k=3), A062318 (k=4), A061547 (k=5), A198306 (k=6), A198307 (k=7), A198308 (k=8), A198309 (k=9), A198310 (k=10), A094626 (k=11); columns: A020725 (g=3), A005843 (g=4), A002522 (g=5), A051890 (g=6), this sequence (g=7). - Jason Kimberley, Oct 30 2011
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KEYWORD
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nonn,easy
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AUTHOR
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Adeniji, Adenike & Makanjuola, Samuel (somakanjuola(AT)unilorin.edu.ng) Apr 14 2011
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EXTENSIONS
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STATUS
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approved
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