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A121470
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Expansion of x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3).
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1
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1, 7, 16, 31, 49, 73, 100, 133, 169, 211, 256, 307, 361, 421, 484, 553, 625, 703, 784, 871, 961, 1057, 1156, 1261, 1369, 1483, 1600, 1723, 1849, 1981, 2116, 2257, 2401, 2551, 2704, 2863, 3025, 3193, 3364, 3541, 3721, 3907, 4096, 4291, 4489, 4693, 4900
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) = 5/8 - 3n/2 + 9n^2/4 + 3*(-1)^n/8.
G.f.: x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3). (End)
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MAPLE
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A121410 := proc(nmin) local M, a, v, wev, wod, n ; a := [] ; M := linalg[matrix](2, 2, [0, 1, -1, 2]) ; v := linalg[vector](2, [1, 7]) ; wev := linalg[vector](2, [0, 3]) ; wod := linalg[vector](2, [0, 6]) ; while nops(a) < nmin do a := [op(a), v[1]] ; n := nops(a)+1 ; v := evalm(M &* v) ; if n mod 2 = 0 then v := evalm(v+wev) ; else v := evalm(v+wod) ; fi ; od: RETURN(a) ; end: A121410(80) ; # R. J. Mathar, Sep 18 2007
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MATHEMATICA
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M := {{0, 1}, {-1, 2} } v[1] = {1, 7} w[n_] = If[Mod[n, 2] == 0, {0, 3}, {0, 6}] v[n_] := v[n] = M.v[n - 1] + w[n] a = Table[v[n][[1]], {n, 1, 30}]
CoefficientList[Series[x (1+5x+2x^2+x^3)/((1+x)(1-x)^3), {x, 0, 50}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {1, 7, 16, 31}, 50] (* Harvey P. Dale, Mar 10 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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