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 A132356 #64 Dec 15 2023 15:29:32
%S A132356 0,8,12,36,44,84,96,152,168,240,260,348,372,476,504,624,656,792,828,
%T A132356 980,1020,1188,1232,1416,1464,1664,1716,1932,1988,2220,2280,2528,2592,
%U A132356 2856,2924,3204,3276,3572,3648,3960,4040,4368,4452,4796,4884,5244,5336,5712
%N A132356 a(2*k) = k*(10*k+2), a(2*k+1) = 10*k^2 + 18*k + 8, with k >= 0.
%C A132356 X values of solutions to the equation 10*X^3 + X^2 = Y^2.
%C A132356 Polygonal number connection: 2*H_n + 6S_n, where H_n is the n-th hexagonal number and S_n is the n-th square number. This is the base formula that is expanded upon to achieve the full series. See contributing formula below. - _William A. Tedeschi_, Sep 12 2010
%C A132356 Equivalently, numbers of the form 2*h*(5*h+1), where h = 0, -1, 1, -2, 2, -3, 3, -4, 4, ... . - _Bruno Berselli_, Feb 02 2017
%H A132356 G. C. Greubel, <a href="/A132356/b132356.txt">Table of n, a(n) for n = 0..1000</a>
%H A132356 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A132356 G.f.: 4*x*(2*x^2+x+2)/((1-x)^3*(1+x)^2). - _R. J. Mathar_, Apr 07 2008
%F A132356 a(n) = 10*x^2 - 2*x, where x = floor(n/2)*(-1)^n for n >= 1. - _William A. Tedeschi_, Sep 12 2010
%F A132356 a(n) = ((2*n+1-(-1)^n)*(10*(2*n+1)-2*(-1)^n))/16. - _Luce ETIENNE_, Sep 13 2014
%F A132356 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 4. - _Chai Wah Wu_, May 24 2016
%F A132356 Sum_{n>=1} 1/a(n) = 5/2 - sqrt(1+2/sqrt(5))*Pi/2. - _Amiram Eldar_, Mar 15 2022
%F A132356 a(n) = n^2 + n + 6*ceiling(n/2)^2. - _Ridouane Oudra_, Aug 06 2022
%t A132356 CoefficientList[Series[4*x*(2*x^2 + x + 2)/((1 - x)^3*(1 + x)^2), {x, 0, 50}], x] (* _G. C. Greubel_, Jun 12 2017 *)
%t A132356 LinearRecurrence[{1,2,-2,-1,1},{0,8,12,36,44},50] (* _Harvey P. Dale_, Dec 15 2023 *)
%o A132356 (PARI) my(x='x+O('x^50)); concat([0], Vec(4*x*(2*x^2+x+2)/((1-x)^3*(1+x)^2))) \\ _G. C. Greubel_, Jun 12 2017
%o A132356 (PARI) a(n) = n^2 + n + 6*((n+1)\2)^2 \\ _Charles R Greathouse IV_, Sep 11 2022
%Y A132356 Cf. A054000, A056220, A087475, A028347, A046092, A132209.
%Y A132356 Cf. numbers m such that k*m+1 is a square: A005563 (k=1), A046092 (k=2), A001082 (k=3), A002378 (k=4), A036666 (k=5), A062717 (k=6), A132354 (k=7), A000217 (k=8), A132355 (k=9), A219257 (k=11), A152749 (k=12), A219389 (k=13), A219390 (k=14), A204221 (k=15), A074378 (k=16), A219394 (k=17), A219395 (k=18), A219396 (k=19), A219190 (k=20), A219391 (k=21), A219392 (k=22), A219393 (k=23), A001318 (k=24), A219259 (k=25), A217441 (k=26), A219258 (k=27), A219191 (k=28).
%Y A132356 Cf. A220082 (numbers k such that 10*k-1 is a square).
%K A132356 nonn,easy
%O A132356 0,2
%A A132356 _Mohamed Bouhamida_, Nov 08 2007
%E A132356 More terms from _Max Alekseyev_, Nov 13 2009