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 A178370 #32 Aug 12 2022 09:22:18
%S A178370 7,25,26,44,133,187,125,161,403,493,296,350,817,943,539,611,1375,1537,
%T A178370 854,944,2077,2275,1241,1349,2923,3157,1700,1826,3913,4183,2231,2375,
%U A178370 5047,5353,2834,2996,6325,6667,3509,3689,7747,8125,4256,4454,9313,9727,5075,5291
%N A178370 The trisection A178242(3n+2).
%C A178370 For n = 0, 1, 2, 3, 4, 5, 6, 7, ...,
%C A178370 a(n-1) = -1, 7, 25, 26, 44, 133, 187, 125, ...
%C A178370 + A177049(n) = 1, 5, 14, 55, 91, 68, 95, 253, ...
%C A178370 gives 0, 12, 39, 81, 135, 201, 282, 378, ...
%C A178370 which are increasing multiples of 3.
%C A178370 a(n) mod 9 = period 4: repeat 7,7,8,8.
%H A178370 G. C. Greubel, <a href="/A178370/b178370.txt">Table of n, a(n) for n = 0..1000</a>
%H A178370 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,10,-12,12,-10,6,-3,1).
%F A178370 a(n) = A060819(2+3*n)*(A060819(7+3*n) + A176672(n+2))/2. - corrected by _G. C. Greubel_, Feb 26 2020
%F A178370 G.f.: (7 +4*x -7*x^2 +46*x^3 -9*x^4 +8*x^5 +4*x^6 +2*x^7 -x^8)/((1-x)^3 * (1 + x^2)^3 ). - _R. J. Mathar_, Jan 16 2011
%F A178370 From _G. C. Greubel_, Feb 26 2020: (Start)
%F A178370 a(n) = (6 + i^n*(1 - i + (-1)^n*(1 + i)))*(9*n^2 + 27*n + 14)/16.
%F A178370 E.g.f.: ( 3*(14+36*x+9*x^2)*exp(x) + (14+36*x-9*x^2)*cos(x) + (14-36*x-9*x^2)*sin(x) )/8. (End)
%F A178370 Sum_{n>=0} 1/a(n) = 1 - (3 + 4*sqrt(3))*Pi/45. - _Amiram Eldar_, Aug 12 2022
%p A178370 m:=50; S:=series((7+4*x-7*x^2+46*x^3-9*x^4+8*x^5+4*x^6+2*x^7-x^8)/((1-x)^3*(1 + x^2)^3 ), x, m+1): seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Feb 26 2020
%t A178370 LinearRecurrence[{3,-6,10,-12,12,-10,6,-3,1}, {7,25,26,44,133,187,125,161,403}, 50] (* _Harvey P. Dale_, May 21 2015 *)
%o A178370 (PARI) Vec( (7+4*x-7*x^2+46*x^3-9*x^4+8*x^5+4*x^6+2*x^7-x^8)/((1-x)^3*(1 + x^2)^3 ) +O('x^50) ) \\ _G. C. Greubel_, Feb 26 2020
%o A178370 (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (7+4*x-7*x^2+46*x^3-9*x^4+8*x^5+4*x^6+2*x^7-x^8)/((1-x)^3*(1 + x^2)^3 ) )); // _G. C. Greubel_, Feb 26 2020
%o A178370 (Sage)
%o A178370 def A178370_list(prec):
%o A178370 P.<x> = PowerSeriesRing(ZZ, prec)
%o A178370 return P( (7+4*x-7*x^2+46*x^3-9*x^4+8*x^5+4*x^6+2*x^7-x^8)/((1-x)^3*(1 + x^2)^3 ) ).list()
%o A178370 A178370_list(50) # _G. C. Greubel_, Feb 26 2020
%Y A178370 Cf. A060819, A176672, A177049.
%K A178370 nonn,easy
%O A178370 0,1
%A A178370 _Paul Curtz_, Dec 21 2010
%E A178370 More terms from _Jinyuan Wang_, Feb 26 2020