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 A081268 #18 Nov 16 2024 12:07:01 %S A081268 1,12,32,61,99,146,202,267,341,424,516,617,727,846,974,1111,1257,1412, %T A081268 1576,1749,1931,2122,2322,2531,2749,2976,3212,3457,3711,3974,4246, %U A081268 4527,4817,5116,5424,5741,6067,6402,6746,7099,7461,7832,8212,8601,8999,9406 %N A081268 Diagonal of triangular spiral in A051682. %H A081268 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A081268 a(n) = C(n,0) + 11*C(n,1) + 9*C(n,2); binomial transform of (1, 11, 9, 0, 0, 0, ...). %F A081268 a(n) = (9*n^2 + 13*n + 2)/2. %F A081268 G.f.: (1 + 9*x - x^2)/(1-x)^3. %F A081268 a(n) = 9*n + a(n-1) + 2 (with a(0)=1). - _Vincenzo Librandi_, Aug 08 2010 %F A081268 From _Elmo R. Oliveira_, Nov 16 2024: (Start) %F A081268 E.g.f.: exp(x)*(9*x^2 + 22*x + 2)/2. %F A081268 a(n) = A064226(n) - 2. %F A081268 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End) %e A081268 a(1) = 9*1 + 1 + 2 = 12. %e A081268 a(2) = 9*2 + 12 + 2 = 32. %e A081268 a(3) = 9*3 + 32 + 2 = 61. %o A081268 (PARI) a(n)=(9*n^2+13*n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017 %Y A081268 Cf. A064226, A081267. %K A081268 easy,nonn %O A081268 0,2 %A A081268 _Paul Barry_, Mar 15 2003