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A295130 a(n) = 3*n*(64*n^2 + 1).

%I A295130 #60 Mar 04 2024 00:19:10
%S A295130 195,1542,5193,12300,24015,41490,65877,98328,139995,192030,255585,
%T A295130 331812,421863,526890,648045,786480,943347,1119798,1316985,1536060,
%U A295130 1778175,2044482,2336133,2654280,3000075,3374670,3779217,4214868,4682775,5184090,5719965,6291552,6900003,7546470,8232105,8958060,9725487
%N A295130 a(n) = 3*n*(64*n^2 + 1).
%D A295130 Martin Gardner, Mathematical Carnival, 1975, Alfred A. Knopf Inc., New York.
%H A295130 Colin Barker, <a href="/A295130/b295130.txt">Table of n, a(n) for n = 1..1000</a>
%H A295130 Stuart Anderson, <a href="http://www.squaring.net/sq/ss/ss.html">Squared squares</a>, 2014
%H A295130 Michael H. Bischoff, <a href="/A295130/a295130_2.pdf">Squares in a square</a>
%H A295130 Wikipedia, <a href="http://www.wikipedia.org/wiki/Squaring_the_square">Squaring the square</a>
%H A295130 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F A295130 a(n) = 3*n*(64*n^2 + 1).
%F A295130 From _Colin Barker_, Nov 23 2017: (Start)
%F A295130 G.f.: 3*x*(65 + 254*x + 65*x^2) / (1 - x)^4.
%F A295130 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A295130 (End)
%F A295130 a(n) = A008585(n) * A158686(n). - _Omar E. Pol_, Nov 24 2017
%F A295130 E.g.f.: 3*x*e^x * (65 + 192*x + 64*x^2). - _Iain Fox_, Dec 22 2017
%e A295130 For examples see "Squares in a square" in the LINKS section.
%t A295130 f[n_] := 3n (64n^2 +1); Array[f, 33] (* or *)
%t A295130 CoefficientList[ Series[(3 (65 +254x +65x^2))/(-1 +x)^4, {x, 0, 33}], x] (* or *)
%t A295130 LinearRecurrence[{4, -6, 4, -1}, {195, 1542, 5193, 12300}, 34] (* _Robert G. Wilson v_, Dec 27 2017 *)
%o A295130 (PARI) Vec(3*x*(65 + 254*x + 65*x^2) / (1 - x)^4 + O(x^40)) \\ _Colin Barker_, Nov 23 2017
%o A295130 (PARI) a(n) = 192*n^3 + 3*n \\ _Iain Fox_, Dec 22 2017
%Y A295130 Cf. A008585, A158686.
%K A295130 nonn,easy
%O A295130 1,1
%A A295130 _Michael H. Bischoff_, Nov 15 2017