This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A195018 #34 Dec 15 2024 19:52:16
%S A195018 0,7,34,81,148,235,342,469,616,783,970,1177,1404,1651,1918,2205,2512,
%T A195018 2839,3186,3553,3940,4347,4774,5221,5688,6175,6682,7209,7756,8323,
%U A195018 8910,9517,10144,10791,11458,12145,12852,13579,14326,15093,15880,16687,17514,18361,19228
%N A195018 a(n) = n*(10*n-3).
%C A195018 Bisection of heptagonal numbers A000566.
%C A195018 Sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This is one of the four semi-diagonals of the square spiral.
%C A195018 Also sequence found by reading the line from 0, in the direction 0, 7, ..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Semi-axis perpendicular to the main axis A195015 in the same spiral.
%H A195018 Vincenzo Librandi, <a href="/A195018/b195018.txt">Table of n, a(n) for n = 0..10000</a>
%H A195018 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A195018 a(n) = A153127(n-1) + 1, if n >= 1.
%F A195018 G.f.: -x*(7+13*x)/(x-1)^3. - _R. J. Mathar_, Oct 15 2011
%F A195018 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=0, a(1)=7, a(2)=34. - _Harvey P. Dale_, May 27 2012
%F A195018 From _Elmo R. Oliveira_, Dec 15 2024: (Start)
%F A195018 E.g.f.: exp(x)*x*(7 + 10*x).
%F A195018 a(n) = A000566(2*n). (End)
%t A195018 Table[n (10 n-3),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,7,34},50] (* _Harvey P. Dale_, May 27 2012 *)
%o A195018 (Magma) [n*(10*n-3): n in [0..50]]; // _Vincenzo Librandi_, Oct 28 2011
%o A195018 (PARI) a(n)=n*(10*n-3) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A195018 Also bisection of A195016.
%Y A195018 Cf. A000566, A033571, A085787, A195013, A195014, A195015, A153127.
%K A195018 nonn,easy
%O A195018 0,2
%A A195018 _Omar E. Pol_, Oct 14 2011