# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a214826 Showing 1-1 of 1 %I A214826 #34 Sep 08 2022 08:46:02 %S A214826 1,4,4,9,17,30,56,103,189,348,640,1177,2165,3982,7324,13471,24777, %T A214826 45572,83820,154169,283561,521550,959280,1764391,3245221,5968892, %U A214826 10978504,20192617,37140013,68311134,125643764,231094911,425049809 %N A214826 a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4. %C A214826 See Comments in A214727. %H A214826 Robert Price, Table of n, a(n) for n = 0..1000 %H A214826 Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. %H A214826 Index entries for linear recurrences with constant coefficients, signature (1,1,1). %F A214826 G.f.: (1+3*x-x^2)/(1-x-x^2-x^3). %F A214826 a(n) = K(n) - 2*T(n+1) + 5*T(n), where K(n) = A001644(n) and T(n) = A000073(n+1). - _G. C. Greubel_, Apr 23 2019 %t A214826 LinearRecurrence[{1,1,1},{1,4,4},33] (* _Ray Chandler_, Dec 08 2013 *) %o A214826 (PARI) my(x='x+O('x^40)); Vec((1+3*x-x^2)/(1-x-x^2-x^3)) \\ _G. C. Greubel_, Apr 23 2019 %o A214826 (Magma) R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+3*x-x^2)/(1-x-x^2-x^3) )); // _G. C. Greubel_, Apr 23 2019 %o A214826 (Sage) ((1+3*x-x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Apr 23 2019 %o A214826 (GAP) a:=[1,4,4];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Apr 23 2019 %Y A214826 Cf. A000213, A000288, A000322, A000383, A060455, A136175, A141036, A141523, A214825-A214831. %K A214826 nonn,easy %O A214826 0,2 %A A214826 _Abel Amene_, Jul 29 2012 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE