cp's OEIS Frontend

A112087 a(n) = 4*(n^2 - n + 1).

%I A112087 #33 Feb 08 2025 18:39:48
%S A112087 4,12,28,52,84,124,172,228,292,364,444,532,628,732,844,964,1092,1228,
%T A112087 1372,1524,1684,1852,2028,2212,2404,2604,2812,3028,3252,3484,3724,
%U A112087 3972,4228,4492,4764,5044,5332,5628,5932,6244,6564,6892,7228,7572,7924,8284
%N A112087 a(n) = 4*(n^2 - n + 1).
%C A112087 Diagonal of a number spiral.
%H A112087 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A112087 a(n) = 4*A002061(n). - _Robert G. Wilson v_, Nov 29 2005
%F A112087 a(n) = 8*n + a(n-1) - 8 (with a(1)=4). - _Vincenzo Librandi_, Nov 13 2010
%F A112087 Sum_{n>=1} 1/a(n) = tanh(Pi*sqrt(3)/2)*Pi/(4*sqrt(3)). - _Amiram Eldar_, Aug 25 2022
%F A112087 From _Elmo R. Oliveira_, Feb 08 2025: (Start)
%F A112087 G.f.: 4*x*(1 + x^2)/(1 - x)^3.
%F A112087 E.g.f.: -4 + 4*exp(x)*(1 + x^2).
%F A112087 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n >= 4. (End)
%e A112087 ..43.44.45.46.47.48.49.50...
%e A112087 ..42.21.22.23.24.25.26.51...
%e A112087 ..40.19..7..8..9.10.27.52...
%e A112087 ..40.19..6..1..2.11.28....
%e A112087 ..39.18..5..4..3.12.29
%e A112087 ..38.17.16.15.14.13.30
%e A112087 ..37.36.35.34.33.32.31
%t A112087 Table[4(n^2 - n + 1), {n, 2, 47}] (* _Robert G. Wilson v_, Nov 29 2005 *)
%o A112087 (Maxima) makelist(4*n^2 - 4*n + 4,n,1,55); /* _Martin Ettl_, Oct 16 2012 */
%o A112087 (PARI) a(n)=4*(n^2-n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A112087 Cf. A002061.
%K A112087 nonn,easy
%O A112087 1,1
%A A112087 Jenny X. Chen (pookahead(AT)gmail.com), Nov 28 2005
%E A112087 Edited and extended by _Robert G. Wilson v_, Nov 29 2005