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 A309717 #34 May 08 2024 11:33:21 %S A309717 0,0,0,1,6,28,114,432,1566,5517,19068,65044,219852,738316,2468028, %T A309717 8222805,27330858,90685224,300521622,994991716,3292117698,10887332473, %U A309717 35992718136,118958691528,393093822744,1298783453112,4290755845176,14174217683209,46821054068430,154655837126740 %N A309717 Convolve Fibonacci, Pell and bronze Fibonacci numbers. %H A309717 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8,-6,8,6,1). %F A309717 G.f.: -x^3/( (x^2+2*x-1) * (x^2+3*x-1) * (x^2+x-1) ) = A006190(x) * A000045(x) * A000129(x). %F A309717 Conjecture: 2*a(n) = A117936(n,3). %F A309717 2*a(n) = A006190(n) + A000045(n) - 2*A000129(n). - _R. J. Mathar_, Mar 10 2023, typo corrected by Xiaoyuan Wang and _Greg Dresden_, May 08 2024 %p A309717 -x^3/( (x^2+2*x-1)*(x^2+3*x-1)*(x^2+x-1) ) ; %p A309717 taylor(%,x=0,30) ; %p A309717 gfun[seriestolist](%) ; %Y A309717 Cf. A006684, A006190 (bronze Fibonacci numbers), A117936. %K A309717 nonn,easy %O A309717 0,5 %A A309717 _R. J. Mathar_, Aug 16 2019