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%I #27 Sep 08 2022 08:44:59
%S 1,9,26,54,95,151,224,316,429,565,726,914,1131,1379,1660,1976,2329,
%T 2721,3154,3630,4151,4719,5336,6004,6725,7501,8334,9226,10179,11195,
%U 12276,13424,14641,15929,17290,18726,20239,21831,23504,25260
%N Rhombi (in 3 different orientations) in a rhombus with 60-degree acute angles.
%C See link for corrections to table in Ask Dr. Math link.
%H Vincenzo Librandi, <a href="/A052153/b052153.txt">Table of n, a(n) for n = 1..1000</a>
%H Ask Dr. Math, <a href="http://mathforum.org/dr.math/problems/arrty25.html">Finding Rhombi in a Rhombus</a>, Source, about 2/3rds down, message dated 01/18/2000.
%H Ray Chandler, <a href="/A052153/a052153_1.txt">Corrections to table in Ask Dr. Math link.</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F a(n) = A000330(n) + A046092(n-1).
%F G.f.: x*(1 + 5*x - 4*x^2)/(1-x)^4. - _Colin Barker_, May 09 2012
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Vincenzo Librandi_, Jun 22 2012
%t Table[n*(n+1)*(2n+1)/6+2n*(n-1),{n,50}] (* Ray Chandler, May 05 2011 *)
%t LinearRecurrence[{4,-6,4,-1},{1,9,26,54},40] (* _Vincenzo Librandi_, Jun 22 2012 *)
%o (Magma) I:=[1, 9, 26, 54]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Jun 22 2012
%Y Cf. A000330, A000537, A006003, A046092.
%K nonn,easy
%O 1,2
%A Tom Gray (TGray9278(AT)aol.com), Jan 24 2000
%E Better description from Larry Reeves (larryr(AT)acm.org), Mar 21 2001
%E Corrected and extended by _Ray Chandler_, May 05 2011
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