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A092076
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Expansion of (1+4*x^3+x^6)/((1-x)*(1-x^3)^2).
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2
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1, 1, 1, 7, 7, 7, 19, 19, 19, 37, 37, 37, 61, 61, 61, 91, 91, 91, 127, 127, 127, 169, 169, 169, 217, 217, 217, 271, 271, 271, 331, 331, 331, 397, 397, 397, 469, 469, 469, 547, 547, 547, 631, 631, 631, 721, 721, 721, 817, 817, 817, 919, 919, 919, 1027, 1027, 1027, 1141, 1141
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: (1+4*x^3+x^6)/((1-x)*(1-x^3)^2).
a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7), n>7. - Wesley Ivan Hurt, Jun 23 2015
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MAPLE
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f:= gfun:-rectoproc({q(n+3)-3*q(n+2)+3*q(n+1)-q(n), q(0) = 1, q(1) = 7, q(2) = 19}, q(n), remember):
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MATHEMATICA
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CoefficientList[Series[(1 + 4*x^3 + x^6)/((1 - x)*(1 - x^3)^2), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 23 2015 *)
LinearRecurrence[{1, 0, 2, -2, 0, -1, 1}, {1, 1, 1, 7, 7, 7, 19}, 60] (* Vincenzo Librandi, Jul 13 2015 *)
With[{c=LinearRecurrence[{3, -3, 1}, {1, 7, 19}, 20]}, {c, c, c}]//Flatten//Sort (* Harvey P. Dale, Aug 03 2019 *)
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PROG
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(Magma) I:=[1, 1, 1, 7, 7, 7, 19]; [n le 7 select I[n] else Self(n-1)+2*Self(n-3)-2*Self(n-4)-Self(n-6)+Self(n-7): n in [1..70]]; // Vincenzo Librandi, Jul 13 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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