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A100182 Structured tetragonal anti-prism numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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: A134747 A083013 A028553 * A321237 A328535 A119515

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

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Last modified February 21 17:15 EST 2020. Contains 332100 sequences. (Running on oeis4.)