%I #34 Sep 01 2024 09:37:06

%S 12,28,44,60,76,92,108,124,140,156,172,188,204,220,236,252,268,284,

%T 300,316,332,348,364,380,396,412,428,444,460,476,492,508,524,540,556,

%U 572,588,604,620,636,652,668,684,700,716,732,748,764,780,796,812,828,844

%N a(n) = 16*n - 4.

%C For n > 3, the number of squares on the infinite 4-column chessboard at <= n knight moves from any fixed start point.

%H Vincenzo Librandi, <a href="/A098502/b098502.txt">Table of n, a(n) for n = 1..5000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%H <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a>.

%F G.f.: 4*x*(3+x)/(1-x)^2. - _Colin Barker_, Jan 09 2012

%F Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi + log(3 - 2*sqrt(2)))/(16*sqrt(2)). - _Amiram Eldar_, Sep 01 2024

%t Range[12, 1000, 16] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%o (Magma) [16*n - 4: n in [1..60]]; // _Vincenzo Librandi_, Jul 24 2011

%o (PARI) a(n)=16*n-4 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Cf. A008590, A017629, A098498, A158953.

%K nonn,easy

%O 1,1

%A _Ralf Stephan_, Sep 15 2004