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A161935
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28-gonal numbers: a(n) = n*(13*n - 12).
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14
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0, 1, 28, 81, 160, 265, 396, 553, 736, 945, 1180, 1441, 1728, 2041, 2380, 2745, 3136, 3553, 3996, 4465, 4960, 5481, 6028, 6601, 7200, 7825, 8476, 9153, 9856, 10585, 11340, 12121, 12928, 13761, 14620, 15505, 16416, 17353, 18316, 19305, 20320, 21361, 22428
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OFFSET
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0,3
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COMMENTS
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The defining formula can be regarded as an approximation and simplification of the expansion / propagation of native hydrophytes on the surface of stagnant waters in orthogonal directions; absence of competition / concurrence and of retrogression is assumed, mortality is taken into account. - [Translation of a comment in French sent by Pierre Gayet]
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LINKS
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FORMULA
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Product_{n>=2} (1 - 1/a(n)) = 13/14. - Amiram Eldar, Jan 22 2021
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EXAMPLE
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G.f. = x + 28*x^2 + 81*x^3 + 160*x^4 + 265*x^5 + 396*x^6 + 553*x^7 + ...
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MATHEMATICA
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lst={}; Do[a=13*n^2+14*n+1; AppendTo[lst, a], {n, 0, 5!}]; lst
Table[n*(13*n - 12), {n, 0, 100}] (* Robert Price, Oct 11 2018 *)
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PROG
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(Magma) [ (n+1)*(13*n+1): n in[0..50] ];
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CROSSREFS
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KEYWORD
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easy,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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