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 A100188 Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence. 15
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..10000 Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1). FORMULA 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 EXAMPLE 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. MATHEMATICA 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 *) PROG (MAGMA) [(1/6)*(2*n^4-2*n^2+6*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011 (PARI) vector(40, n, (n^4 -n^2 +3*n)/3) \\ G. C. Greubel, Nov 08 2018 CROSSREFS Cf. A000578, A000447, A004466, A007588, A063521, A062523 - "polar" structured anti-diamonds; A100189 - "equatorial" structured meta-anti-diamond numbers; A006484 for other structured meta numbers; and A100145 for more on structured numbers. Sequence in context: A217365 A124089 A250283 * A131985 A125196 A100189 Adjacent sequences:  A100185 A100186 A100187 * A100189 A100190 A100191 KEYWORD nonn,easy AUTHOR James A. Record (james.record(AT)gmail.com), Nov 07 2004 STATUS approved

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Last modified January 20 02:13 EST 2019. Contains 319320 sequences. (Running on oeis4.)