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 A134594 #29 Sep 08 2022 08:45:32 %S A134594 5,16,29,44,61,80,101,124,149,176,205,236,269,304,341,380,421,464,509, %T A134594 556,605,656,709,764,821,880,941,1004,1069,1136,1205,1276,1349,1424, %U A134594 1501,1580,1661,1744,1829,1916,2005,2096,2189,2284,2381,2480,2581,2684 %N A134594 a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5. %C A134594 (1+sqrt(n))^5 = (5*n^2 + 10*n + 1) + (n^2 + 10*n + 5)*sqrt(n). For coefficients of the rational part see A134593. %H A134594 G. C. Greubel, <a href="/A134594/b134594.txt">Table of n, a(n) for n = 0..1000</a> %H A134594 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1). %F A134594 a(n) = ((1+sqrt(n))^5 - (5*n^2 + 10*n + 1))/sqrt(n), for n > 0. [corrected by _Jon E. Schoenfield_, Nov 23 2018] %F A134594 G.f.: (1+x)*(5-4*x)/(1-x)^3. - _R. J. Mathar_, Nov 14 2007 %F A134594 a(n) = 2*n + a(n-1) + 9 (with a(0)=5). - _Vincenzo Librandi_, Nov 23 2010 %F A134594 E.g.f.: (5 +11*x +x^2)*exp(x). - _G. C. Greubel_, Nov 23 2018 %t A134594 Table[(n^2 + 10n + 5), {n, 0, 50}] %t A134594 LinearRecurrence[{3,-3,1}, {5,16,29}, 50] (* _G. C. Greubel_, Nov 23 2018 *) %o A134594 (PARI) a(n)=n^2+10*n+5 \\ _Charles R Greathouse IV_, Jun 17 2017 %o A134594 (Magma) [n^2 +10*n +5: n in [0..50]]; // _G. C. Greubel_, Nov 23 2018 %o A134594 (Sage) [n^2 +10*n +5 for n in range(50)] # _G. C. Greubel_, Nov 23 2018 %o A134594 (GAP) List([0..50],n->n^2+10*n+5); # _Muniru A Asiru_, Nov 24 2018 %Y A134594 Cf. A134593. %K A134594 nonn,easy %O A134594 0,1 %A A134594 _Artur Jasinski_, Nov 04 2007