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 A262927 #22 Sep 08 2022 08:46:14
%S A262927 0,1,3,6,10,15,23,30,39,49,60,72,85,99,114,132,149,168,188,209,231,
%T A262927 254,278,303,331,358,387,417,448,480,513,547,582,620,657,696,736,777,
%U A262927 819,862,906,951,999,1046,1095,1145,1196,1248,1301,1355,1410,1468,1525
%N A262927 a(n+9) = a(n) + 10*(n+4) + 9. a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=10, a(5)=15, a(6)=23, a(7)=30, a(8)=39.
%C A262927 The main (or principal) sequence for the 11 steps recurrence is 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 30, 33, 36, ..., the partial sums of A054898.
%C A262927 a(n) mod 9 is a sequence of period 90.
%H A262927 Colin Barker, <a href="/A262927/b262927.txt">Table of n, a(n) for n = 0..1000</a>
%H A262927 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
%F A262927 a(n) = A262397(2n) + A262397(2n+1).
%F A262927 a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11), n>10.
%F A262927 G.f.: -x*(x^8+2*x^7-x^6+3*x^5+x^4+x^3+x^2+x+1) / ((x-1)^3*(x^2+x+1)*(x^6+x^3+1)). - _Colin Barker_, Oct 04 2015
%F A262927 a(n) = (5n^2 + 4n)/9 + O(1), or more precisely (5n^2 + 4n + 3)/9 <= a(n) <= (5n^2 + 4n - 10)/9. - _Charles R Greathouse IV_, Oct 16 2015
%t A262927 LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 1, 3, 6, 10, 15, 23, 30, 39, 49, 60}, 60] (* _Vincenzo Librandi_, Oct 06 2015 *)
%t A262927 RecurrenceTable[{a[n+9] == a[n] + 10*(n+4) + 9, a[0]=0, a[1]=1, a[2]=3, a[3]=6, a[4]=10, a[5]=15, a[6]=23, a[7]=30, a[8]=39},a,{n,0,1000}] (* _G. C. Greubel_, Oct 16 2015 *)
%o A262927 (PARI) a(n) = numerator(((2*n)^2+4)/4)\9 + numerator(((2*n+1)^2+4)/4)\9;
%o A262927 vector(100, n, a(n-1)) \\ _Altug Alkan_, Oct 04 2015
%o A262927 (PARI) concat(0, Vec(-x*(x^8+2*x^7-x^6+3*x^5+x^4+x^3+x^2+x+1)/((x-1)^3*(x^2+x+1)*(x^6+x^3+1)) + O(x^100))) \\ _Colin Barker_, Oct 04 2015
%o A262927 (PARI) a(n)=((2*n+1)^2+4)\9+(n^2+1)\9 \\ _Charles R Greathouse IV_, Oct 16 2015
%o A262927 (Magma) I:=[0,1,3,6,10,15,23,30,39]; [n le 9 select I[n] else (Self(n-9)+10*(n-6)+9): n in [1..60]]; // _Vincenzo Librandi_, Oct 06 2015
%Y A262927 Cf. A054898, A261327, A262397.
%K A262927 nonn,easy,less
%O A262927 0,3
%A A262927 _Paul Curtz_, Oct 04 2015