cp's OEIS Frontend

A131640 First differences are periodic: 50, 50, 75, 50, 50, 75, ...

%I A131640 #33 Sep 09 2025 08:12:52
%S A131640 985,1035,1085,1160,1210,1260,1335,1385,1435,1510,1560,1610,1685,1735,
%T A131640 1785,1860,1910,1960,2035,2085,2135,2210,2260,2310,2385,2435,2485,
%U A131640 2560,2610,2660,2735,2785,2835,2910,2960,3010,3085,3135,3185,3260,3310,3360
%N A131640 First differences are periodic: 50, 50, 75, 50, 50, 75, ...
%H A131640 Harvey P. Dale, <a href="/A131640/b131640.txt">Table of n, a(n) for n = 0..1000</a>
%H A131640 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A131640 G.f.: 5*(197 + 10*x + 10*x^2 - 182*x^3)/((1-x)^2*(1+x+x^2)). - _R. J. Mathar_, Nov 14 2007
%F A131640 From _G. C. Greubel_, Sep 08 2025: (Start)
%F A131640 a(n) = (5/3)*(35*(n+1) + 551 + 5*(A102283(n+1) + A102283(n))).
%F A131640 a(n) = (5/3)*(35*n + 586 + 5*A057078(n)).
%F A131640 E.g.f.: (5/3)*( 5*exp(-x/2)*( cos((sqrt(3)*x)/2) + (1/sqrt(3))*sin((sqrt(3)*x)/2)) + (586 + 35*x)*exp(x) ). (End)
%p A131640 A131640 := proc(n) option remember ; if n =0 then 985 ; elif n mod 3 = 0 then A131640(n-1)+75 ; else A131640(n-1)+50 ; fi ; end: seq(A131640(n),n=0..80) ; # _R. J. Mathar_, Oct 24 2007
%t A131640 LinearRecurrence[{1,0,1,-1},{985,1035,1085,1160},50] (* _Ray Chandler_, Aug 25 2015 *)
%t A131640 Table[5*(35*n +591 -5*Mod[n,3])/3, {n,0,50}] (* _G. C. Greubel_, Sep 08 2025 *)
%o A131640 (PARI) Vec(5*(197+10*x+10*x^2-182*x^3)/((1-x)^2*(1+x+x^2)) + O(x^40)) \\ _Andrew Howroyd_, Feb 20 2018
%o A131640 (Magma)
%o A131640 A131640:= func< n | (5/3)*(35*n + 591 - 5*(n mod 3) ) >;
%o A131640 [A131640(n): n in [0..50]]; // _G. C. Greubel_, Sep 08 2025
%o A131640 (SageMath)
%o A131640 def A131640(n): return 5*(35*n + 591 - 5*(n%3))//3
%o A131640 print([A131640(n) for n in range(51)]) # _G. C. Greubel_, Sep 08 2025
%Y A131640 Cf. A057078, A102283.
%K A131640 nonn,easy,changed
%O A131640 0,1
%A A131640 Eric M. Adler (eadler(AT)simi.k12.ca.us), Sep 05 2007
%E A131640 Definition supplied by _N. J. A. Sloane_, Sep 14 2007
%E A131640 More terms from _R. J. Mathar_, Oct 24 2007