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A166873 a(n) = a(n-1) + 12*n for n > 1; a(1) = 1.

%I A166873 #15 Sep 08 2022 08:45:48
%S A166873 1,25,61,109,169,241,325,421,529,649,781,925,1081,1249,1429,1621,1825,
%T A166873 2041,2269,2509,2761,3025,3301,3589,3889,4201,4525,4861,5209,5569,
%U A166873 5941,6325,6721,7129,7549,7981,8425,8881,9349,9829,10321,10825,11341,11869
%N A166873 a(n) = a(n-1) + 12*n for n > 1; a(1) = 1.
%C A166873 Binomial transform of 1,24,12,0,0,0,....
%H A166873 Vincenzo Librandi, <a href="/A166873/b166873.txt">Table of n, a(n) for n = 1..1000</a>
%H A166873 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A166873 a(n) = 6*n^2 + 6*n - 11.
%F A166873 a(n) = 2*a(n-1) - a(n-2) + 12.
%F A166873 G.f.: x*(1 + 22*x - 11*x^2)/(1-x)^3.
%F A166873 a(n) - a(n-1) = A008594(n) for n > 1.
%F A166873 From _G. C. Greubel_, May 27 2016: (Start)
%F A166873 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A166873 E.g.f.: (-11 + 12*x + 6*x^2)*exp(x) + 11. (End)
%t A166873 LinearRecurrence[{3,-3,1},{1,25,61},50] (* _G. C. Greubel_, May 27 2016 *)
%o A166873 (Magma) [ n eq 1 select 1 else Self(n-1)+12*n: n in [1..44] ];
%o A166873 (PARI) a(n)=6*n^2+6*n-11 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A166873 Cf. A008594 (multiples of 12).
%Y A166873 A000217, A028387, A133694, A059993, A166137, A166143, A166146, A166147, A166148, A166150, A166144 have recurrence a(n-1)+k*n with a(1)=1 or a(0)=1 for k = 1..11 resp.
%K A166873 easy,nonn
%O A166873 1,2
%A A166873 _Klaus Brockhaus_, Oct 22 2009