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A143859 Ulam's spiral (WNW spoke).

%I A143859 #33 Sep 08 2022 08:45:38
%S A143859 1,18,67,148,261,406,583,792,1033,1306,1611,1948,2317,2718,3151,3616,
%T A143859 4113,4642,5203,5796,6421,7078,7767,8488,9241,10026,10843,11692,12573,
%U A143859 13486,14431,15408,16417,17458,18531,19636,20773,21942,23143,24376
%N A143859 Ulam's spiral (WNW spoke).
%C A143859 Also sequence found by reading the segment (1, 18) together with the line from 18, in the direction 18, 67, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 05 2012
%H A143859 Harvey P. Dale, <a href="/A143859/b143859.txt">Table of n, a(n) for n = 1..1000</a>
%H A143859 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A143859 a(n) = 16*n^2 - 31*n + 16. - _R. J. Mathar_, Sep 08 2008
%F A143859 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), a(1)=1, a(2)=18, a(3)=67. - _Harvey P. Dale_, Mar 24 2012
%F A143859 G.f.: x*(1 + 15*x + 16*x^2)/(1-x)^3. - _Colin Barker_, Aug 03 2012
%F A143859 E.g.f.: -16 + (16 - 15*x + 16*x^2)*exp(x). - _G. C. Greubel_, Nov 09 2019
%p A143859 seq( ((32*n-31)^2+63)/64, n=1..50); # _G. C. Greubel_, Nov 09 2019
%t A143859 f[n_]:= 16n^2 -31n +16; Array[f, 40] (* _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008 *)
%t A143859 LinearRecurrence[{3,-3,1},{1,18,67},40] (* _Harvey P. Dale_, Mar 24 2012 *)
%t A143859 CoefficientList[Series[(1+15x+16x^2)/(1-x)^3, {x,0,40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%o A143859 (Magma) [16*n^2-31*n+16: n in [1..50]]; // _Vincenzo Librandi_, Nov 08 2014
%o A143859 (PARI) vector(50, n, 16*n^2-31*n+16) \\ _Michel Marcus_, Nov 08 2014
%o A143859 (Sage) [((32*n-31)^2+63)/64 for n in (1..50)] # _G. C. Greubel_, Nov 09 2019
%o A143859 (GAP) List([1..50], n-> ((32*n-31)^2+63)/64); # _G. C. Greubel_, Nov 09 2019
%K A143859 nonn,easy
%O A143859 1,2
%A A143859 _Vladimir Joseph Stephan Orlovsky_, Sep 03 2008