A178370 The trisection A178242(3n+2).
7, 25, 26, 44, 133, 187, 125, 161, 403, 493, 296, 350, 817, 943, 539, 611, 1375, 1537, 854, 944, 2077, 2275, 1241, 1349, 2923, 3157, 1700, 1826, 3913, 4183, 2231, 2375, 5047, 5353, 2834, 2996, 6325, 6667, 3509, 3689, 7747, 8125, 4256, 4454, 9313, 9727, 5075, 5291
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (3,-6,10,-12,12,-10,6,-3,1).
Programs
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Magma
R
:=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 -
Maple
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
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Mathematica
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 *) -
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 -
Sage
def A178370_list(prec): P.
= PowerSeriesRing(ZZ, prec) 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() A178370_list(50) # G. C. Greubel, Feb 26 2020
Formula
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
From G. C. Greubel, Feb 26 2020: (Start)
a(n) = (6 + i^n*(1 - i + (-1)^n*(1 + i)))*(9*n^2 + 27*n + 14)/16.
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)
Sum_{n>=0} 1/a(n) = 1 - (3 + 4*sqrt(3))*Pi/45. - Amiram Eldar, Aug 12 2022
Extensions
More terms from Jinyuan Wang, Feb 26 2020
Comments