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A100188
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Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence.
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15
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1, 6, 27, 84, 205, 426, 791, 1352, 2169, 3310, 4851, 6876, 9477, 12754, 16815, 21776, 27761, 34902, 43339, 53220, 64701, 77946, 93127, 110424, 130025, 152126, 176931, 204652, 235509, 269730, 307551, 349216
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = (1/6)*(2*n^4 - 2*n^2 + 6*n).
G.f.: x*(1 + x + 7*x^2 - x^3)/(1-x)^5. - Colin Barker, Apr 16 2012
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(1)=1, a(2)=6, a(3)=27, a(4)=84, a(5)=205. - Harvey P. Dale, May 11 2016
E.g.f.: (3*x + 6*x^2 + 6*x^3 + x^4)*exp(x)/3. - G. C. Greubel, Nov 08 2018
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EXAMPLE
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There are no 1- or 2-gonal anti-diamonds, so 1 and (2n+2) are the first and second terms since all the sequences begin as such.
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MATHEMATICA
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Table[(2n^4-2n^2+6n)/6, {n, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 6, 27, 84, 205}, 40] (* Harvey P. Dale, May 11 2016 *)
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PROG
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(PARI) vector(40, n, (n^4 -n^2 +3*n)/3) \\ G. C. Greubel, Nov 08 2018
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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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James A. Record (james.record(AT)gmail.com), Nov 07 2004
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STATUS
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approved
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