OFFSET
0,1
COMMENTS
Also the number for Waterman [polyhedra] have a unit rhombic dodecahedron face so sqrt 4, sqrt 20, sqrt 52, etc...and a one-to-one match...that is, no omissions and no extras. - Steve Waterman and Roger Kaufman (swaterman(AT)watermanpolyhedron.com), Apr 02 2009. [This sentence makes no sense - some words must have been dropped. - N. J. A. Sloane, Jun 12 2014]
Also, sequence found by reading the segment (4,20) together with the line from 20, in the direction 20, 52, ..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Sep 04 2011
Sum of consecutive even squares: (2*n)^2 + (2*n + 2)^2 = 8*n^2 + 8*n + 4. - Michel Marcus, Jan 27 2014
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Adrian Rossiter, Antiprism.
Steve Waterman, Polyhedra Project.
Steve Waterman, Waterman's Polyhedral Mensuration chart.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 8*n^2 + 8*n + 4.
G.f.: 4*(1+2*x+x^2)/(1-x)^3.
a(n) = 16*n + a(n-1), a(0)=4. - Vincenzo Librandi, Nov 13 2010
a(n) = A069129(n+1) + 3. - Omar E. Pol, Sep 04 2011
a(n) = A035008(n) + 4. - Omar E. Pol, Jun 12 2014
From Elmo R. Oliveira, Oct 27 2024: (Start)
E.g.f.: 4*(1 + 4*x + 2*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
MAPLE
MATHEMATICA
CoefficientList[Series[-(4*(z^2 + 2*z + 1))/(z - 1)^3, {z, 0, 100}], z] (* and *) Table[8*n*(n + 1) + 4, {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *)
PROG
(PARI) a(n)=8*n^2+8*n+4 \\ Charles R Greathouse IV, Jul 17 2011
(Magma) [ 8*n^2 + 8*n + 4 : n in [0..50] ]; // Wesley Ivan Hurt, Jun 09 2014
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005
STATUS
approved