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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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
KEYWORD
easy,nonn
AUTHOR
James A. Record (james.record(AT)gmail.com), Nov 07 2004
STATUS
approved