A100177 Structured meta-prism numbers, the n-th number from a structured n-gonal prism number sequence.

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

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 A362316 A255611

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