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 A122709 #49 Mar 07 2023 18:50:45
%S A122709 1,6,15,24,33,42,51,60,69,78,87,96,105,114,123,132,141,150,159,168,
%T A122709 177,186,195,204,213,222,231,240,249,258,267,276,285,294,303,312,321,
%U A122709 330,339,348,357,366,375,384,393,402,411,420,429,438,447,456,465,474,483
%N A122709 a(0)=1; thereafter a(n) = 9*n - 3.
%C A122709 Self-convolution of A122553.
%H A122709 Colin Barker, <a href="/A122709/b122709.txt">Table of n, a(n) for n = 0..1000</a>
%H A122709 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A122709 a(0)=1, a(n) = 9*n - 3 = A008591(n) - 3 for n > 0.
%F A122709 a(n) = 2*a(n-1) - a(n-2) for n > 2; a(0)=1, a(1)=6, a(2)=15.
%F A122709 a(n) = a(n-1) + 9 for n > 1; a(0)=1, a(1)=6.
%F A122709 G.f.: ((1 + 2*x)/(1 - x))^2.
%F A122709 Equals binomial transform of [1, 5, 4, -4, 4, -4, 4, ...]. - _Gary W. Adamson_, Dec 10 2007
%F A122709 a(n) = A017233(n-1) for n > 0. - _Georg Fischer_, Oct 21 2018
%F A122709 E.g.f.: exp(x)*(9*x - 3) + 4. - _Stefano Spezia_, Mar 07 2023
%p A122709 seq(coeff(series(((1+2*x)/(1-x))^2,x,n+1), x, n), n = 0 .. 60); # _Muniru A Asiru_, Oct 21 2018
%t A122709 Join[{1},LinearRecurrence[{2,-1},{6,15},60]] (* _Harvey P. Dale_, Jun 12 2012 *)
%o A122709 (PARI) a(n)=max(9*n-3,1) \\ _Charles R Greathouse IV_, Jan 17 2012
%o A122709 (PARI) Vec((1 + 2*x)^2 / (1 - x)^2 + O(x^100)) \\ _Colin Barker_, Jan 22 2018
%o A122709 (GAP) a:=[6,15];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; Concatenation([1],a); # _Muniru A Asiru_, Oct 21 2018
%Y A122709 Cf. A017233 (9n+6), A008591, A122553.
%K A122709 nonn,easy
%O A122709 0,2
%A A122709 _Philippe Deléham_, Sep 23 2006
%E A122709 Edited by _N. J. A. Sloane_, Jan 23 2018