A192809
Coefficient of x in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
Original entry on oeis.org
0, 0, 2, 14, 74, 366, 1786, 8702, 42410, 206734, 1007834, 4913310, 23953034, 116774190, 569289402, 2775359806, 13530239338, 65961672910, 321571716762, 1567703857118, 7642759781962, 37259445922414, 181644634930298, 885541171698814
Offset: 0
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a:=[0,0,2];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # Muniru A Asiru, Jan 02 2019
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m:=30; R:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( 2*x^2/(1-7*x+12*x^2-8*x^3) )); // G. C. Greubel, Jan 02 2019
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(See A192808.)
LinearRecurrence[{7,-12,8}, {0,0,2}, 30] (* G. C. Greubel, Jan 02 2019 *)
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my(x='x+O('x^30)); concat([0,0], Vec(2*x^2/(1-7*x+12*x^2-8*x^3))) \\ G. C. Greubel, Jan 02 2019
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(2*x^2/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 02 2019
Original entry on oeis.org
0, 0, 1, 7, 37, 183, 893, 4351, 21205, 103367, 503917, 2456655, 11976517, 58387095, 284644701, 1387679903, 6765119669, 32980836455, 160785858381, 783851928559, 3821379890981, 18629722961207, 90822317465149, 442770585849407
Offset: 0
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a:=[0,0,1];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # Muniru A Asiru, Jan 03 2019
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m:=30; R:=PowerSeriesRing(Integers(), m); [0,0] cat Coefficients(R!( x^2/(1-7*x+12*x^2-8*x^3) )); // G. C. Greubel, Jan 03 2019
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(See A192808.)
LinearRecurrence[{7,-12,8},{0,0,1},30] (* Harvey P. Dale, Dec 06 2018 *)
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my(x='x+O('x^30)); concat([0,0], Vec(x^2/(1-7*x+12*x^2-8*x^3))) \\ G. C. Greubel, Jan 03 2019
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(x^2/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 03 2019
A192810
Coefficient of x^2 in the reduction of the polynomial (x^2 + 2)^n by x^3 -> x^2 + 2.
Original entry on oeis.org
0, 1, 5, 23, 109, 527, 2565, 12503, 60957, 297183, 1448821, 7063207, 34434061, 167870511, 818390501, 3989759863, 19450597117, 94824185471, 462280211797, 2253676033863, 10986963179245, 53562871542735, 261125950919109, 1273022903354903
Offset: 0
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a:=[0,1,5];; for n in [4..25] do a[n]:=7*a[n-1]-12*a[n-2]+8*a[n-3]; od; Print(a); # Muniru A Asiru, Jan 02 2019
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m:=30; R:=PowerSeriesRing(Integers(), m); [0] cat Coefficients(R!( x*(1-2*x)/(1-7*x+12*x^2-8*x^3) )); // G. C. Greubel, Jan 02 2019
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(See A192808.)
LinearRecurrence[{7,-12,8}, {0,1,5}, 30] (* G. C. Greubel, Jan 02 2019 *)
CoefficientList[Series[x (1-2x)/(1-7x+12x^2-8x^3),{x,0,30}],x] (* Harvey P. Dale, Aug 26 2021 *)
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my(x='x+O('x^30)); concat([0], Vec(x*(1-2*x)/(1-7*x+12*x^2-8*x^3) )) \\ G. C. Greubel, Jan 02 2019
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(x*(1-2*x)/(1-7*x+12*x^2-8*x^3)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Jan 02 2019
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