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 A139619 #31 Apr 17 2024 03:42:15 %S A139619 19,190,361,532,703,874,1045,1216,1387,1558,1729,1900,2071,2242,2413, %T A139619 2584,2755,2926,3097,3268,3439,3610,3781,3952,4123,4294,4465,4636, %U A139619 4807,4978,5149,5320,5491,5662,5833,6004,6175,6346,6517,6688 %N A139619 a(n) = 171*n + 19. %C A139619 Numbers of the 19th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 19th column in the square array A057145. %H A139619 Vincenzo Librandi, <a href="/A139619/b139619.txt">Table of n, a(n) for n = 0..5000</a> %H A139619 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1). %F A139619 From _Chai Wah Wu_, Apr 14 2017: (Start) %F A139619 a(n) = 2*a(n-1) - a(n-2) for n > 1. %F A139619 G.f.: (152*x + 19)/(x - 1)^2. (End) %F A139619 From _Elmo R. Oliveira_, Apr 11 2024: (Start) %F A139619 E.g.f.: 19*exp(x)*(1 + 9*x). %F A139619 a(n) = 19*A017173(n) = 19*(A051682(n+1) - A051682(n)). (End) %t A139619 Range[0, 100]*171 + 19 (* _Paolo Xausa_, Apr 17 2024 *) %o A139619 (Magma) [19*(9*n + 1): n in [0..50]]; // _Vincenzo Librandi_, Jul 23 2011 %o A139619 (PARI) a(n)=171*n+19 \\ _Charles R Greathouse IV_, Oct 05 2011 %Y A139619 Cf. A016957, A017329, A057145, A139600, A139606-A139618, A139620. %Y A139619 Cf. A017173, A051682. %K A139619 easy,nonn %O A139619 0,1 %A A139619 _Omar E. Pol_, May 21 2008