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A008813
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Expansion of (1+x^6)/((1-x)^2*(1-x^6)).
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11
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1, 2, 3, 4, 5, 6, 9, 12, 15, 18, 21, 24, 29, 34, 39, 44, 49, 54, 61, 68, 75, 82, 89, 96, 105, 114, 123, 132, 141, 150, 161, 172, 183, 194, 205, 216, 229, 242, 255, 268, 281, 294, 309, 324, 339, 354, 369, 384, 401, 418, 435, 452, 469, 486, 505, 524, 543, 562
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OFFSET
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0,2
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COMMENTS
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Number of 0..n arrays of 7 elements with zero second differences. - R. H. Hardin, Nov 16 2011
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LINKS
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FORMULA
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G.f.: (1+x^6)/((1-x)^2*(1-x^6)).
a(n) = 2*a(n-1) -a(n-2) +a(n-6) -2*a(n-7) +a(n-8). - R. H. Hardin, Nov 16 2011
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MAPLE
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seq(coeff(series((1+x^6)/((1-x)^2*(1-x^6)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 12 2019
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MATHEMATICA
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CoefficientList[Series[(1+x^6)/(1-x)^2/(1-x^6), {x, 0, 70}], x] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 4, 5, 6, 9, 12}, 70] (* Harvey P. Dale, Oct 13 2012 *)
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PROG
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(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^6)/((1-x)^2*(1-x^6)) )); // G. C. Greubel, Sep 12 2019
(Sage)
P.<x> = PowerSeriesRing(ZZ, prec)
return P((1+x^6)/((1-x)^2*(1-x^6))).list()
(GAP) a:=[1, 2, 3, 4, 5, 6, 9, 12];; for n in [9..70] do a[n]:=2*a[n-1]-a[n-2] +a[n-6]-2*a[n-7]+a[n-8]; od; a; # G. C. Greubel, Sep 12 2019
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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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EXTENSIONS
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STATUS
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approved
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