%I #28 Sep 08 2022 08:45:15

%S 1,4,18,64,175,396,784,1408,2349,3700,5566,8064,11323,15484,20700,

%T 27136,34969,44388,55594,68800,84231,102124,122728,146304,173125,

%U 203476,237654,275968,318739,366300,418996,477184,541233,611524,688450,772416,863839,963148,1070784,1187200,1312861,1448244

%N Structured meta-prism numbers, the n-th number from a structured n-gonal prism number sequence.

%H Vincenzo Librandi, <a href="/A100177/b100177.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F a(n) = (1/6)*(3*n^4 - 9*n^3 + 12*n^2).

%F G.f.: x*(1 - x + 8*x^2 + 4*x^3)/(1-x)^5. - _Colin Barker_, Jun 08 2012

%F a(n) = A060354(n) * n = A000124(n-2) * n^2. - _Bruce J. Nicholson_, Jul 11 2018

%e 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.

%t 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 *)

%o (PARI) a(n)=(1/6)*(3*n^4-9*n^3+12*n^2);

%o (Magma) [(1/6)*(3*n^4-9*n^3+12*n^2): n in [1..50] ]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A002411, A000578, A050509, A006597, A100176, A100177 - structured prisms; A006484 for other meta structured numbers; and A100145 for more on structured numbers.

%Y Cf. A060354, A000124.

%K easy,nonn

%O 1,2

%A James A. Record (james.record(AT)gmail.com), Nov 07 2004