A008598 - OEIS

%I #53 Jul 16 2022 01:25:37

%S 0,16,32,48,64,80,96,112,128,144,160,176,192,208,224,240,256,272,288,

%T 304,320,336,352,368,384,400,416,432,448,464,480,496,512,528,544,560,

%U 576,592,608,624,640,656,672,688,704,720,736,752,768,784,800,816,832

%N Multiples of 16.

%C If X is an n-set and Y_i (i=1,2,3,4) mutually disjoint 2-subsets of X then a(n-6) is equal to the number of 5-subsets of X intersecting each Y_i (i=1,2,3,4). - _Milan Janjic_, Aug 26 2007

%H Vincenzo Librandi, <a href="/A008598/b008598.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=328">Encyclopedia of Combinatorial Structures 328</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>

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

%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

%H Leo Tavares, <a href="/A008598/a008598.jpg">Illustration: Square Block Star Frames</a>

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

%F a(n) = Sum_{k=1..8n} (i^k+1)*(i^(8n-k)+1), where i=sqrt(-1). - _Bruno Berselli_, Mar 19 2012

%F G.f.: 16*x/(x-1)^2. - _Vincenzo Librandi_, Jun 10 2013

%F a(n) = A014641(n) - A185212(n). - _Leo Tavares_, May 24 2022

%p A008598:=n->16*n; seq(A008598(n), n=0..100); # _Wesley Ivan Hurt_, Nov 13 2013

%t Range[0, 1000, 16] (* _Vladimir Joseph Stephan Orlovsky_, May 31 2011 *)

%t CoefficientList[Series[16 x / (x - 1)^2, {x, 0, 60}], x] (* _Vincenzo Librandi_ Jun 10 2013 *)

%o (PARI) a(n)=16*n \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A008596, A008597.

%Y Cf. A014641, A185212.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_