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A005998
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Number of paraffins.
(Formerly M1740)
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1
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1, 2, 7, 14, 29, 48, 79, 116, 169, 230, 311, 402, 517, 644, 799, 968, 1169, 1386, 1639, 1910, 2221, 2552, 2927, 3324, 3769, 4238, 4759, 5306, 5909, 6540, 7231, 7952, 8737, 9554, 10439, 11358, 12349, 13376, 14479, 15620, 16841, 18102, 19447, 20834, 22309
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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G.f.: x*(x^4+2*x^3+2*x^2+1)/(-1+x)^2/(-1+x^2)^2.
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MAPLE
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a:= n-> (Matrix([[0, -1, -4, -11, -22, -41]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -4, 1, 2, -1][i] else 0 fi)^n)[1, 1]:
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MATHEMATICA
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CoefficientList[Series[(x^4 + 2 x^3 + 2 x^2 + 1)/(-1 + x)^2/(-1 + x^2)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 15 2014 *)
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PROG
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(Magma) [1/8*(2*n^3-2*n^2+5*n-(-1)^n*(n+1)+1): n in [1..50]]; // Vincenzo Librandi, Mar 15 2014
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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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