This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108099 #63 Oct 28 2024 18:55:43
%S A108099 4,20,52,100,164,244,340,452,580,724,884,1060,1252,1460,1684,1924,
%T A108099 2180,2452,2740,3044,3364,3700,4052,4420,4804,5204,5620,6052,6500,
%U A108099 6964,7444,7940,8452,8980,9524,10084,10660,11252,11860,12484,13124,13780,14452,15140,15844
%N A108099 a(n) = 8*n^2 + 8*n + 4.
%C A108099 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]
%C A108099 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
%C A108099 Sum of consecutive even squares: (2*n)^2 + (2*n + 2)^2 = 8*n^2 + 8*n + 4. - _Michel Marcus_, Jan 27 2014
%H A108099 Ivan Panchenko, <a href="/A108099/b108099.txt">Table of n, a(n) for n = 0..1000</a>
%H A108099 Adrian Rossiter, <a href="http://www.antiprism.com/programs/waterman.html">Antiprism</a>.
%H A108099 Steve Waterman, <a href="http://watermanpolyhedron.com/polyhedra.html">Polyhedra Project</a>.
%H A108099 Steve Waterman, <a href="http://watermanpolyhedron.com/MENSrhdZZZ.html">Waterman's Polyhedral Mensuration chart</a>.
%H A108099 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A108099 a(n) = 8*n^2 + 8*n + 4.
%F A108099 G.f.: 4*(1+2*x+x^2)/(1-x)^3.
%F A108099 a(n) = 16*n + a(n-1), a(0)=4. - _Vincenzo Librandi_, Nov 13 2010
%F A108099 a(n) = A069129(n+1) + 3. - _Omar E. Pol_, Sep 04 2011
%F A108099 a(n) = A035008(n) + 4. - _Omar E. Pol_, Jun 12 2014
%F A108099 From _Elmo R. Oliveira_, Oct 27 2024: (Start)
%F A108099 E.g.f.: 4*(1 + 4*x + 2*x^2)*exp(x).
%F A108099 a(n) = 4*A001844(n) = 2*A069894(n).
%F A108099 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%p A108099 A108099:=n->8*n^2 + 8*n + 4; seq(A108099(n), n=0..50); # _Wesley Ivan Hurt_, Jun 09 2014
%t A108099 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 *)
%o A108099 (PARI) a(n)=8*n^2+8*n+4 \\ _Charles R Greathouse IV_, Jul 17 2011
%o A108099 (Magma) [ 8*n^2 + 8*n + 4 : n in [0..50] ]; // _Wesley Ivan Hurt_, Jun 09 2014
%Y A108099 Cf. A000217, A001844, A016742, A035008, A069129, A069894.
%K A108099 nonn,easy
%O A108099 0,1
%A A108099 Dorthe Roel (dorthe_roel(AT)hotmail.com or dorthe.roel1(AT)skolekom.dk), Jun 07 2005