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 A276026 #17 Sep 15 2022 02:20:03
%S A276026 140,204,284,380,492,620,764,924,1100,1292,1500,1724,1964,2220,2492,
%T A276026 2780,3084,3404,3740,4092,4460,4844,5244,5660,6092,6540,7004,7484,
%U A276026 7980,8492,9020,9564,10124,10700,11292,11900,12524,13164,13820,14492,15180,15884,16604,17340,18092,18860,19644,20444,21260,22092,22940
%N A276026 a(n) = Sum_{k=0..7} (n + k)^2.
%C A276026 Sums of eight consecutive squares.
%C A276026 More generally, the ordinary generating function for the sums of m consecutive squares of nonnegative integers is m*(1 - 2*x + 13*x^2 + 2*m^2 (1 - 2*x + x^2) - 3*m*(1 - 4*x + 3*x^2))/(6*(1 - x)^3).
%H A276026 G. C. Greubel, <a href="/A276026/b276026.txt">Table of n, a(n) for n = 0..1000</a>
%H A276026 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%H A276026 <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>.
%F A276026 O.g.f.: 4*(35 - 54*x + 23*x^2)/(1 - x)^3.
%F A276026 E.g.f.: 4*(35 + 16*x + 2*x^2)*exp(x).
%F A276026 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F A276026 a(-n) = a(n-7).
%F A276026 a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2 + (n+6)^2 + (n+7)^2.
%F A276026 a(n) = 8*n^2 + 56*n + 140.
%F A276026 Sum_{n>=0} 1/a(n) = tanh(sqrt(21)*Pi/2)*Pi/(8*sqrt(21)) - 763/15180. - _Amiram Eldar_, Sep 15 2022
%e A276026 a(0) = 0^2 + 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 140;
%e A276026 a(1) = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 = 204;
%e A276026 a(2) = 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 = 284, etc.
%t A276026 Table[8 n^2 + 56 n + 140, {n, 0, 50}]
%t A276026 LinearRecurrence[{3, -3, 1}, {140, 204, 284}, 51]
%o A276026 (PARI) a(n)=8*n^2+56*n+140 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A276026 (Magma) [4*(2*n^2 +14*n +35): n in [0..60]]; // _G. C. Greubel_, Aug 24 2022
%o A276026 (SageMath) [4*(2*n^2 +14*n +35) for n in (0..60)] # _G. C. Greubel_, Aug 24 2022
%Y A276026 Cf. A000290, A001844, A027575, A027578, A027865, A120328, A260637.
%Y A276026 Cf. A001844, A005918.
%K A276026 nonn,easy
%O A276026 0,1
%A A276026 _Ilya Gutkovskiy_, Aug 16 2016