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A037205
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a(n) = (n+1)^n - 1.
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12
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0, 1, 8, 63, 624, 7775, 117648, 2097151, 43046720, 999999999, 25937424600, 743008370687, 23298085122480, 793714773254143, 29192926025390624, 1152921504606846975, 48661191875666868480, 2185911559738696531967, 104127350297911241532840, 5242879999999999999999999, 278218429446951548637196400, 15519448971100888972574851071
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OFFSET
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0,3
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COMMENTS
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For n >= 1, a(n) = order of Fibonacci group F(n+1,n).
The terms, written in base n+1, are n digits of value n. For example, a(4) = 624 = 4444 in base 5. - Marc Morgenegg, Nov 30 2016
For n >= 1, in a square grid of side n, this is the number of ways to populate the grid with 1 X 1 blocks (with at least one block) so that no block falls under the effect of gravity. - Paolo Xausa, Apr 12 2021
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REFERENCES
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D. L. Johnson, Presentation of Groups, Cambridge, 1976, p. 182.
Richard M. Thomas, The Fibonacci groups revisited, in Groups - St. Andrews 1989, Vol. 2, 445-454, London Math. Soc. Lecture Note Ser., 160, Cambridge Univ. Press, Cambridge, 1991.
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LINKS
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FORMULA
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MATHEMATICA
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Table[(n + 1)^n - 1, {n, 0, 21}] (* or *)
Table[If[n < 1, Length@ #, FromDigits[#, n + 1]] &@ ConstantArray[n, n], {n, 0, 21}] (* Michael De Vlieger, Nov 30 2016 *)
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PROG
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(PARI) for(n=0, 25, print1((n + 1)^n - 1, ", ")) \\ G. C. Greubel, Nov 10 2017
(Magma) [(n + 1)^n - 1: n in [0..25]]; // G. C. Greubel, Nov 10 2017
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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