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A033572 a(n) = (2*n+1)*(7*n+1).

%I A033572 #29 Jan 03 2025 18:26:57
%S A033572 1,24,75,154,261,396,559,750,969,1216,1491,1794,2125,2484,2871,3286,
%T A033572 3729,4200,4699,5226,5781,6364,6975,7614,8281,8976,9699,10450,11229,
%U A033572 12036,12871,13734,14625,15544,16491,17466,18469,19500,20559,21646,22761,23904,25075,26274,27501,28756
%N A033572 a(n) = (2*n+1)*(7*n+1).
%C A033572 Sequence found by reading the line from 1, in the direction 1, 24,..., in the square spiral whose vertices are the generalized enneagonal numbers A118277. Also sequence found by reading the same line in the square spiral whose edges have length A195019 and whose vertices are the numbers A195020. - _Omar E. Pol_, Sep 13 2011
%H A033572 G. C. Greubel, <a href="/A033572/b033572.txt">Table of n, a(n) for n = 0..1000</a>
%H A033572 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A033572 a(n) = a(n-1) + 28*n - 5 for n>0, a(0)=1. - _Vincenzo Librandi_, Nov 17 2010
%F A033572 From _G. C. Greubel_, Oct 12 2019: (Start)
%F A033572 G.f.: (1 + 21*x + 6*x^2)/(1-x)^3.
%F A033572 E.g.f.: (1 + 23*x + 14*x^2)*exp(x). (End)
%F A033572 Sum 1/a(n) = -gamma/5 -2*log(2)/5 -psi(1/7)/5 = 1.0800940432405839438217..., gamma=A001620, psi(1/7) = -A354627. - _R. J. Mathar_, May 07 2024
%p A033572 seq((2*n+1)*(7*n+1), n=0..50); # _G. C. Greubel_, Oct 12 2019
%t A033572 Table[(2*n+1)*(7*n+1), {n, 0, 50}] (* _G. C. Greubel_, Oct 12 2019 *)
%t A033572 LinearRecurrence[{3,-3,1},{1,24,75},50] (* _Harvey P. Dale_, Apr 19 2023 *)
%o A033572 (PARI) a(n)=(2*n+1)*(7*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A033572 (Magma) [(2*n+1)*(7*n+1): n in [0..50]]; // _G. C. Greubel_, Oct 12 2019
%o A033572 (Sage) [(2*n+1)*(7*n+1) for n in range(50)] # _G. C. Greubel_, Oct 12 2019
%o A033572 (GAP) List([0..50], n-> (2*n+1)*(7*n+1)); # _G. C. Greubel_, Oct 12 2019
%Y A033572 Bisection of A001106.
%K A033572 nonn,easy
%O A033572 0,2
%A A033572 _N. J. A. Sloane_