(MAGMAMagma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^3-x^4+x^10 +x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) )); // G. C. Greubel, Feb 06 2020

editing

approved

1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 3, 1, 4, 2, 5, 5, 7, 4, 10, 8, 12, 12, 16, 13, 24, 21, 27, 27, 35, 34, 48, 45, 54, 57, 72, 70, 90, 88, 104, 112, 132, 132, 159, 162, 188, 199, 228, 230, 270, 281, 316, 333, 373, 384, 441, 458, 506, 532, 590, 613

# p/q = 1 +x^12 +x^20 +2*x^24 +x^28 +..., where

seq(coeff(series(p/q, x, 2*n+1), x, 2*n), n=0..60);

proposed

editing

editing

proposed

G.f.: (1 -x^3 -x^4 +x^10 +x^11 +x^12 +x^16 -x^19 -x^23 +x^26 +x^30 +x^31 +x^32 -x^38 -x^39 +x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)). - G. C. Greubel, Feb 06 2020

p/q = 1 +x^12 +x^20 +2*x^24 +x^28 +..., where

p := x^140 +x^110 +x^108 +x^106 +2*x^104 +2*x^102 +3*x^100 +3*x^98 +3*x^96 +3*x^94 +4*x^92 +4*x^90 +4*x^88 +4*x^86 +4*x^84 +4*x^82 +4*x^80 +4*x^78 +3*x^76 +4*x^74 +3*x^72 +4*x^70 +3*x^68 +4*x^66 +3*x^64 +4*x^62 +4*x^60 +4*x^58 +4*x^56 +4*x^54 +4*x^52 +4*x^50 +4*x^48 +3*x^46 +3*x^44 +3*x^42 +3*x^40 +2*x^38 +2*x^36 +x^34 +x^32 +x^30 +1;

4*x^90+4*x^88+4*x^86+4*x^84+4*x^82+4*x^80+4*x^78+3*x^76+4*x^74+3*x^72+4*x^70+

3*x^68+4*x^66+3*x^64+4*x^62+4*x^60+4*x^58+4*x^56+4*x^54+4*x^52+4*x^50+4*x^48+

3*x^46+3*x^44+3*x^42+3*x^40+2*x^38+2*x^36+x^34+x^32+x^30+1;

CoefficientList[Series[(1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)), {x, 0, 60}], x] (* G. C. Greubel, Feb 06 2020 *)

(PARI) Vec( (1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) +O('x^60) ) \\ G. C. Greubel, Feb 06 2020

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x^3-x^4+x^10 +x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) )); // G. C. Greubel, Feb 06 2020

(Sage)

def A005813_list(prec):

P.<x> = PowerSeriesRing(ZZ, prec)

return P( (1-x^3-x^4+x^10+x^11+x^12+x^16-x^19-x^23+x^26+x^30+x^31 +x^32-x^38-x^39+x^42)/((1-x^3)*(1-x^4)*(1-x^6)*(1-x^7)*(1-x^10)*(1-x^15)) ).list()

A005813_list(60) # G. C. Greubel, Feb 06 2020

approved

editing

editing

approved

Ray Chandler, <a href="/A005813/b005813.txt">Table of n, a(n) for n = 0..1000</a>

<a href="/index/Rec#order_45">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 1, 1, 0, 1, 0, 0, -1, -1, -1, 0, -1, 0, 1, 0, 1, -1, 0, 1, 0, 0, 0, 0, 1, 0, -1, 1, 0, 1, 0, -1, 0, -1, -1, -1, 0, 0, 1, 0, 1, 1, 0, 0, -1).

approved

editing

proposed

approved

editing

proposed