A100182 Structured tetragonal anti-prism numbers.

1, 8, 28, 68, 135, 236, 378, 568, 813, 1120, 1496, 1948, 2483, 3108, 3830, 4656, 5593, 6648, 7828, 9140, 10591, 12188, 13938, 15848, 17925, 20176, 22608, 25228, 28043, 31060, 34286, 37728, 41393, 45288, 49420, 53796, 58423, 63308, 68458, 73880, 79581, 85568, 91848, 98428, 105315, 112516

Offset

1,2

Comments

If offset is changed to 0, this is the number of magic labelings of the 5-node, 8-edge graph formed from a square with both diagonals drawn and a node at the center [Stanley]. - N. J. A. Sloane, Jul 07 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (1/6)*(7*n^3 - 3*n^2 + 2*n). [Corrected by Luca Colucci, Mar 01 2011]

G.f.: x*(1 + 4*x + 2*x^2)/(1-x)^4. - Colin Barker, Jun 08 2012

E.g.f.: (6*x +18*x^2 +7*x^3)*exp(x)/6. - G. C. Greubel, Nov 08 2018

a(n) = binomial(n,3) + n^3. - Pedro Caceres, Jul 28 2019

Mathematica

Table[(7*n^3 - 3*n^2 + 2*n)/6, {n, 1, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 8, 28, 68}, 40] (* G. C. Greubel, Nov 08 2018 *)

Prog

(Magma) [(1/6)*(7*n^3-3*n^2+2*n): n in [1..40]]; // Vincenzo Librandi, Aug 18 2011
(PARI) vector(40, n, (7*n^3 -3*n^2 +2*n)/6) \\ G. C. Greubel, Nov 08 2018

Crossrefs

Cf. A100185 - structured anti-prisms; A100145 for more on structured numbers.

Sequence in context: A083013 A350144 A028553 * A321237 A328535 A358247

Adjacent sequences: A100179 A100180 A100181 * A100183 A100184 A100185

Keyword

easy,nonn

Author

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

Status

approved