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%I #16 Oct 24 2016 01:40:46
%S 15,33,65,105,153,209,273,345,425,513,609,713,825,945,1073,1209,1353,
%T 1505,1665,1833,2009,2193,2385,2585,2793,3009,3233,3465,3705,3953,
%U 4209,4473,4745,5025,5313,5609,5913,6225,6545,6873,7209,7553,7905,8265,8633,9009
%N Records in A277384.
%C Essentially the same as A145923. - _R. J. Mathar_, Oct 23 2016
%H Colin Barker, <a href="/A277385/b277385.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(15 -12*x +11*x^2 -6*x^3) / (1-x)^3.
%F E.g.f.: 7 + 6*x + (4*x^2 + 16*x - 7)*exp(x). - _G. C. Greubel_, Oct 12 2016
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.
%F a(n) = 4*n^2 + 12*n - 7 for n>1.
%t Join[{15}, LinearRecurrence[{3, -3, 1}, {33, 65, 105}, 25]] (* or *) Join[{15}, Table[4*n^2 + 12*n - 7, {n,2,25}]] (* _G. C. Greubel_, Oct 12 2016 *)
%o (PARI) Vec(x*(15-12*x+11*x^2-6*x^3)/(1-x)^3 + O(x^60))
%Y Cf. A277384.
%K nonn,easy
%O 1,1
%A _Colin Barker_, Oct 12 2016
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