A108099 a(n) = 8n^2 + 8n + 4.

4, 20, 52, 100, 164, 244, 340, 452, 580, 724, 884, 1060, 1252, 1460, 1684, 1924, 2180, 2452, 2740, 3044, 3364, 3700, 4052, 4420, 4804, 5204, 5620, 6052, 6500, 6964, 7444, 7940, 8452, 8980, 9524, 10084, 10660, 11252, 11860, 12484, 13124, 13780, 14452, 15140

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

Maple

A108099:=n->8*n^2 + 8*n + 4; seq(A108099(n), n=0..50); # Wesley Ivan Hurt, Jun 09 2014

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

Cf. A016742.

Sequence in context: A187274 A367915 A368112 * A244050 A250224 A250272

Adjacent sequences: A108096 A108097 A108098 * A108100 A108101 A108102

Keyword

nonn,easy

Author

Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005

Status

approved