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 A100177 Structured meta-prism numbers, the n-th number from a structured n-gonal prism number sequence. 9
 1, 4, 18, 64, 175, 396, 784, 1408, 2349, 3700, 5566, 8064, 11323, 15484, 20700, 27136, 34969, 44388, 55594, 68800, 84231, 102124, 122728, 146304, 173125, 203476, 237654, 275968, 318739, 366300, 418996, 477184, 541233, 611524, 688450, 772416, 863839, 963148, 1070784, 1187200, 1312861, 1448244 (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)*(3*n^4 - 9*n^3 + 12*n^2). G.f.: x*(1 - x + 8*x^2 + 4*x^3)/(1-x)^5. - Colin Barker, Jun 08 2012 a(n) = A060354(n) * n = A000124(n-2) * n^2. - Bruce J. Nicholson, Jul 11 2018 EXAMPLE There are no 1- or 2-gonal prisms, so 1 and (2n) are used as the first and second terms since all the sequences begin as such. MATHEMATICA Table[(3n^4-9n^3+12n^2)/6, {n, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 4, 18, 64, 175}, 50] (* Harvey P. Dale, Nov 07 2017 *) PROG (PARI) a(n)=(1/6)*(3*n^4-9*n^3+12*n^2); (MAGMA) [(1/6)*(3*n^4-9*n^3+12*n^2): n in [1..50] ]; // Vincenzo Librandi, Aug 02 2011 CROSSREFS Cf. A002411, A000578, A050509, A006597, A100176, A100177 - structured prisms; A006484 for other meta structured numbers; and A100145 for more on structured numbers. Cf. A060354, A000124. Sequence in context: A057414 A165910 A212766 * A083321 A255611 A022728 Adjacent sequences:  A100174 A100175 A100176 * A100178 A100179 A100180 KEYWORD easy,nonn AUTHOR James A. Record (james.record(AT)gmail.com), Nov 07 2004 STATUS approved

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Last modified August 25 16:31 EDT 2019. Contains 326324 sequences. (Running on oeis4.)