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A143839 Ulam's spiral (SSE spoke).

%I A143839 #41 Sep 08 2022 08:45:38
%S A143839 1,24,79,166,285,436,619,834,1081,1360,1671,2014,2389,2796,3235,3706,
%T A143839 4209,4744,5311,5910,6541,7204,7899,8626,9385,10176,10999,11854,12741,
%U A143839 13660,14611,15594,16609,17656,18735,19846,20989,22164,23371,24610
%N A143839 Ulam's spiral (SSE spoke).
%C A143839 Also sequence found by reading the line from 1, in the direction 1, 24, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H A143839 Harvey P. Dale, <a href="/A143839/b143839.txt">Table of n, a(n) for n = 1..1000</a>
%H A143839 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A143839 a(n) = 16*n^2 - 25*n + 10. - _R. J. Mathar_, Sep 04 2008
%F A143839 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1) = 1, a(2) = 24, a(3) = 79. - _Harvey P. Dale_, May 26 2012
%F A143839 G.f.: x*(1 + 21*x + 10*x^2)/(1-x)^3. - _Harvey P. Dale_, May 26 2012
%F A143839 E.g.f.: exp(x)*(10 - 9*x + 16*x^2) - 9. - _Stefano Spezia_, Oct 07 2019
%p A143839 seq( ((32*n -25)^2 +15)/64, n=1..40); # _G. C. Greubel_, Nov 09 2019
%t A143839 f[n_] := 16n^2 -25n +10; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008 *)
%t A143839 LinearRecurrence[{3,-3,1},{1,24,79},40] (* _Harvey P. Dale_, May 26 2012 *)
%t A143839 CoefficientList[Series[(1+21*x+10*x^2)/(1-x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%o A143839 (Magma) [16*n^2-25*n+10: n in [1..40]]; // _Vincenzo Librandi_, Nov 08 2014
%o A143839 (PARI) Vec(x*(1+21*x+10*x^2)/(1-x)^3 + O(x^40)) \\ _Colin Barker_, Nov 08 2014
%o A143839 (Sage) [((32*n -25)^2 +15)/64 for n in (1..40)] # _G. C. Greubel_, Nov 09 2019
%o A143839 (GAP) List([1..40], n-> ((32*n -25)^2 +15)/64); # _G. C. Greubel_, Nov 09 2019
%Y A143839 Cf. A004767, A016813.
%K A143839 nonn,easy
%O A143839 1,2
%A A143839 _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008