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1, 0, 2, 1, 0, 6, 10, 20, 35, 50, 84, 105, 168, 196, 300, 336, 495, 540, 770, 825, 1144, 1210, 1638, 1716, 2275, 2366, 3080, 3185, 4080, 4200, 5304, 5440, 6783, 6936, 8550, 8721, 10640, 10830, 13090, 13300, 15939, 16170, 19228, 19481, 23000, 23276, 27300
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1 -x -2*x^2 +3*x^3 -3*x^4 +4*x^5 +16*x^6 -16*x^7 -14*x^8 +14*x^9 +4*x^10 -4*x^11 )/((1+x)^4*(1-x)^5). - Colin Barker, Mar 15 2013
a(n) = abs((2*n^4 +12*n^3 -2*n^2 -132*n -195 +(4*n^3 -6*n^2 -124*n -189)*(-1)^n))/384. - Luce ETIENNE, Jun 01 2015
a(n) = abs((-3*(65 +63*(-1)^n) -4*(33 +31*(-1)^n)*n -2*(1+3*(-1)^n)*n^2 +4*(3 +(-1)^n)*n^3 +2*n^4)/384). - Colin Barker, Jun 02 2015
a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) - 6*a(n-4) + 6*a(n-5) + 4*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9) for n > 11. - Charles R Greathouse IV, Jun 02 2015
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MATHEMATICA
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f[n_]:= n*(n+1)*(n+2)*(n-3)/12; g[n_]:= n^2*(n^2 -1)/12; Table[{Abs[f[n]], g[n]}, {n, 1, 25}]//Flatten
LinearRecurrence[{1, 4, -4, -6, 6, 4, -4, -1, 1}, {1, 0, 2, 1, 0, 6, 10, 20, 35, 50, 84, 105}, 50] (* Harvey P. Dale, Mar 05 2016 *)
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PROG
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(PARI) my(x='x+O('x^50)); Vec((1-x-2*x^2+3*x^3-3*x^4+4*x^5+16*x^6-16*x^7 -14*x^8+14*x^9+4*x^10-4*x^11 )/((1+x)^4*(1-x)^5)) \\ G. C. Greubel, May 19 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1-x -2*x^2+3*x^3-3*x^4+4*x^5+16*x^6-16*x^7 -14*x^8+14*x^9+4*x^10-4*x^11 )/( (1+x)^4*(1-x)^5) )); // G. C. Greubel, May 19 2019
(Sage) ((1-x-2*x^2+3*x^3-3*x^4+4*x^5+16*x^6-16*x^7 -14*x^8+14*x^9+4*x^10 -4*x^11 )/((1+x)^4*(1-x)^5)).series(x, 50).coefficients(x, sparse=False) # G. C. Greubel, May 19 2019
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CROSSREFS
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KEYWORD
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nonn,less,easy
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AUTHOR
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STATUS
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approved
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