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A321180 a(n) = 17*n^2 - 1.

%I A321180 #24 Jan 16 2025 12:11:59
%S A321180 -1,16,67,152,271,424,611,832,1087,1376,1699,2056,2447,2872,3331,3824,
%T A321180 4351,4912,5507,6136,6799,7496,8227,8992,9791,10624,11491,12392,13327,
%U A321180 14296,15299,16336,17407,18512,19651,20824,22031,23272,24547,25856,27199,28576,29987
%N A321180 a(n) = 17*n^2 - 1.
%C A321180 a(n) mod 9 = period 9: repeat [8, 7, 4, 8, 1, 1, 8, 4, 7] = A254375(n+5).
%C A321180 1020 = 2*2*15*17.
%H A321180 Colin Barker, <a href="/A321180/b321180.txt">Table of n, a(n) for n = 0..1000</a>
%H A321180 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A321180 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A321180 a(n) = A244630(n) - 1.
%F A321180 a(n+1) = a(n) + 17*(2n+1).
%F A321180 a(n+10) = a(n) + 10*A061085(n+5).
%F A321180 a(n+15) = a(15-n) + 1020*n.
%F A321180 G.f.: (1 - 19*x - 16*x^2)/(-1 + x)^3. - _Stefano Spezia_, Oct 29 2018
%F A321180 E.g.f.: exp(x)*(17*x^2 + 17*x - 1). - _Elmo R. Oliveira_, Jan 16 2025
%t A321180 a[n_]:=17*n^2 - 1; Array[a, 50] (* or *)
%t A321180 CoefficientList[Series[(1 - 19 x - 16 x^2)/(-1 + x)^3, {x, 0, 50}], x] (* _Stefano Spezia_, Oct 29 2018 *)
%t A321180 LinearRecurrence[{3,-3,1},{-1,16,67},40] (* _Harvey P. Dale_, Jul 03 2021 *)
%o A321180 (PARI) a(n)=17*n^2-1 \\ _Charles R Greathouse IV_, Oct 30 2018
%o A321180 (PARI) Vec((1 - 19*x - 16*x^2)/(-1 + x)^3 + O(x^50)) \\ _Colin Barker_, Oct 31 2018
%Y A321180 Cf. A000079, A005408, A061085, A244630, A254375.
%K A321180 sign,easy,less
%O A321180 0,2
%A A321180 _Paul Curtz_, Oct 29 2018
%E A321180 One term corrected by _Colin Barker_, Oct 29 2018