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 A016994 #26 May 07 2024 06:29:47 %S A016994 1,64,225,484,841,1296,1849,2500,3249,4096,5041,6084,7225,8464,9801, %T A016994 11236,12769,14400,16129,17956,19881,21904,24025,26244,28561,30976, %U A016994 33489,36100,38809,41616,44521,47524 %N A016994 a(n) = (7*n + 1)^2. %H A016994 Vincenzo Librandi, <a href="/A016994/b016994.txt">Table of n, a(n) for n = 0..10000</a> %H A016994 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A016994 G.f.: (1 + 61*x + 36*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jan 27 2013 %F A016994 From _G. C. Greubel_, Dec 28 2022: (Start) %F A016994 a(2*n) = A134934(n). %F A016994 a(2*n+1) = 4*A017030(n). %F A016994 E.g.f.: (1 + 63*x + 49*x^2)*exp(x). (End) %F A016994 Sum_{n>=0} 1/a(n) = Psi'(1/7)/49 = 1.027703498712483534.. - _R. J. Mathar_, May 07 2024 %t A016994 (7Range[0,50]+1)^2 (* _Harvey P. Dale_, Mar 05 2011 *) %t A016994 CoefficientList[Series[(1+61*x+36*x^2)/(1-x)^3, {x,0,40}], x] (* _Vincenzo Librandi_, Jan 27 2013 *) %o A016994 (Magma) [(7*n+1)^2: n in [0..40]]; // _Vincenzo Librandi_, Jul 13 2011 %o A016994 (PARI) a(n)=(7*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017 %o A016994 (SageMath) [(7*n+1)^2 for n in range(41)] # _G. C. Greubel_, Dec 28 2022 %Y A016994 Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m-3), A016814 (m=4), A016862 (m=5), A016922 (m=6), this sequence (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14). %K A016994 nonn,easy %O A016994 0,2 %A A016994 _N. J. A. Sloane_