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 A195142 #59 Jan 16 2023 08:52:52
%S A195142 0,1,10,21,40,61,90,121,160,201,250,301,360,421,490,561,640,721,810,
%T A195142 901,1000,1101,1210,1321,1440,1561,1690,1821,1960,2101,2250,2401,2560,
%U A195142 2721,2890,3061,3240,3421,3610,3801,4000,4201,4410,4621,4840,5061,5290
%N A195142 Concentric 10-gonal numbers.
%C A195142 Also concentric decagonal numbers. Also sequence found by reading the line from 0, in the direction 0, 10, ..., and the same line from 1, in the direction 1, 21, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. Main axis, perpendicular to A028895 in the same spiral.
%H A195142 Vincenzo Librandi, <a href="/A195142/b195142.txt">Table of n, a(n) for n = 0..10000</a>
%H A195142 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F A195142 G.f.: -x*(1+8*x+x^2) / ( (1+x)*(x-1)^3 ). - _R. J. Mathar_, Sep 18 2011
%F A195142 a(n) = -a(n-1) + 5*n^2 - 5*n + 1, a(0)=0. - _Vincenzo Librandi_, Sep 27 2011
%F A195142 From _Bruno Berselli_, Sep 27 2011: (Start)
%F A195142 a(n) = a(-n) = (10*n^2 + 3*(-1)^n - 3)/4.
%F A195142 a(n) = a(n-2) + 10*(n-1). (End)
%F A195142 a(n) = 2*a(n-1) + 0*a(n-2) - 2*a(n-3) + a(n-4); a(0)=0, a(1)=1, a(2)=10, a(3)=21. - _Harvey P. Dale_, Sep 29 2011
%F A195142 Sum_{n>=1} 1/a(n) = Pi^2/60 + tan(sqrt(3/5)*Pi/2)*Pi/(2*sqrt(15)). - _Amiram Eldar_, Jan 16 2023
%t A195142 RecurrenceTable[{a[0]==0,a[1]==1,a[n]==a[n-2]+10(n-1)},a[n],{n,50}] (* or *) LinearRecurrence[{2,0,-2,1},{0,1,10,21},50] (* _Harvey P. Dale_, Sep 29 2011 *)
%o A195142 (Magma) [(10*n^2+3*(-1)^n-3)/4: n in [0..50]]; // _Vincenzo Librandi_, Sep 27 2011
%o A195142 (Haskell)
%o A195142 a195142 n = a195142_list !! n
%o A195142 a195142_list = scanl (+) 0 a090771_list
%o A195142 -- _Reinhard Zumkeller_, Jan 07 2012
%Y A195142 A033583 and A069133 interleaved.
%Y A195142 Cf. A028895, A032527, A032528, A077221, A085787, A195042, A195143, A195145, A195146, A195147, A195148, A195149.
%Y A195142 Cf. A090771 (first differences).
%Y A195142 Column 10 of A195040. - _Omar E. Pol_, Sep 28 2011
%K A195142 nonn,easy
%O A195142 0,3
%A A195142 _Omar E. Pol_, Sep 17 2011