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%I #37 Aug 23 2022 06:25:21
%S 1,18,55,112,189,286,403,540,697,874,1071,1288,1525,1782,2059,2356,
%T 2673,3010,3367,3744,4141,4558,4995,5452,5929,6426,6943,7480,8037,
%U 8614,9211,9828,10465,11122,11799,12496,13213,13950,14707,15484,16281,17098,17935,18792,19669,20566,21483
%N a(n) = (2*n + 1)*(5*n + 1).
%C Sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the diagonals in the spiral. - _Omar E. Pol_, Sep 10 2011
%C Also sequence found by reading the line from 1, in the direction 1, 18, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. This is a line perpendicular to the main axis A195015 in the same spiral. - _Omar E. Pol_, Oct 14 2011
%H G. C. Greubel, <a href="/A033571/b033571.txt">Table of n, a(n) for n = 0..1000</a>
%H Leo Tavares, <a href="/A033571/a033571.jpg">Illustration: Stellar Layers</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = A153126(2*n) = A000566(2*n+1). - _Reinhard Zumkeller_, Dec 20 2008
%F From _Reinhard Zumkeller_, Mar 13 2009: (Start)
%F a(n) = A008596(n) + A158186(n), for n > 0.
%F a(n) = A010010(n) - A158186(n). (End)
%F a(n) = a(n-1) + 20*n - 3 (with a(0)=1). - _Vincenzo Librandi_, Nov 17 2010
%F From _G. C. Greubel_, Oct 12 2019: (Start)
%F G.f.: (1 + 15*x + 4*x^2)/(1-x)^3.
%F E.g.f.: (1 + 17*x + 10*x^2)*exp(x). (End)
%F a(n) = A003154(n+1) + A007742(n). - _Leo Tavares_, Mar 27 2022
%F Sum_{n>=0} 1/a(n) = sqrt(1+2/sqrt(5))*Pi/6 + sqrt(5)*log(phi)/6 + 5*log(5)/12 - 2*log(2)/3, where phi is the golden ratio (A001622). - _Amiram Eldar_, Aug 23 2022
%p seq((2*n+1)*(5*n+1), n=0..50); # _G. C. Greubel_, Oct 12 2019
%t Table[(2*n+1)*(5*n+1), {n,0,50}] (* _G. C. Greubel_, Oct 12 2019 *)
%o (PARI) a(n)=(2*n+1)*(5*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Magma) [(2*n+1)*(5*n+1): n in [0..50]] # _G. C. Greubel_, Oct 12 2019
%o (Sage) [(2*n+1)*(5*n+1) for n in range(50)] # _G. C. Greubel_, Oct 12 2019
%o (GAP) List([0..50], n-> (2*n+1)*(5*n+1)); # _G. C. Greubel_, Oct 12 2019
%Y Cf. A153127. - _Reinhard Zumkeller_, Dec 20 2008
%Y Cf. A000566, A008596, A010010, A153126, A158186.
%Y Cf. A001622, A003154, A007742, A019952.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E Terms a(36) onward added by _G. C. Greubel_, Oct 12 2019
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