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A016898 a(n) = (5*n + 4)^2.

%I A016898 #26 Feb 16 2025 08:32:33
%S A016898 16,81,196,361,576,841,1156,1521,1936,2401,2916,3481,4096,4761,5476,
%T A016898 6241,7056,7921,8836,9801,10816,11881,12996,14161,15376,16641,17956,
%U A016898 19321,20736,22201,23716,25281,26896,28561,30276,32041,33856,35721,37636,39601,41616
%N A016898 a(n) = (5*n + 4)^2.
%C A016898 If Y is a fixed 2-subset of a (5n+1)-set X then a(n-1) is the number of 3-subsets of X intersecting Y. - _Milan Janjic_, Oct 21 2007
%C A016898 Interleaving of A017318 and A017378. - _Michel Marcus_, Aug 26 2015
%H A016898 Vincenzo Librandi, <a href="/A016898/b016898.txt">Table of n, a(n) for n = 0..1000</a>
%H A016898 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>.
%H A016898 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PolygammaFunction.html">Polygamma Function</a>.
%H A016898 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polygamma_function">Polygamma Function</a>.
%H A016898 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A016898 From _Colin Barker_, Mar 30 2017: (Start)
%F A016898 G.f.: (16 + 33*x + x^2) / (1 - x)^3.
%F A016898 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
%F A016898 (End)
%F A016898 Sum_{n>=0} 1/a(n) = polygamma(1, 4/5)/25. - _Amiram Eldar_, Oct 02 2020
%e A016898 a(0) = (5*0 + 4)^2 = 16.
%t A016898 Table[(5*n + 4)^2, {n, 0, 25}] (* _Amiram Eldar_, Oct 02 2020 *)
%t A016898 LinearRecurrence[{3,-3,1},{16,81,196},50] (* _Harvey P. Dale_, Jul 30 2023 *)
%o A016898 (Magma) [(5*n+4)^2: n in [0..70]]; // _Vincenzo Librandi_, May 02 2011
%o A016898 (PARI) Vec((16 + 33*x + x^2) / (1 - x)^3 + O(x^40)) \\ _Colin Barker_, Mar 30 2017
%Y A016898 Cf. A016850, A016862, A016874, A016886.
%K A016898 nonn,easy
%O A016898 0,1
%A A016898 _N. J. A. Sloane_