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A168547
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a(n) = 1 - 2*n^2 + 4*n*(1 + 2*n^2)/3.
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4
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1, 3, 17, 59, 145, 291, 513, 827, 1249, 1795, 2481, 3323, 4337, 5539, 6945, 8571, 10433, 12547, 14929, 17595, 20561, 23843, 27457, 31419, 35745, 40451, 45553, 51067, 57009, 63395, 70241, 77563, 85377, 93699, 102545, 111931, 121873, 132387, 143489, 155195
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OFFSET
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0,2
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COMMENTS
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Binomial transform of the quasi-finite sequence 1,2,12,16,0,... (0 continued).
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LINKS
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FORMULA
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a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
G.f.: (1 - x + 11*x^2 + 5*x^3)/(x-1)^4.
First differences: a(n+1) - a(n) = 2*A054569(n+1).
Second differences: a(n+2) - 2*a(n+1) + a(n) = 4*A004767(n).
Third differences: a(n+3) - 3*a(n+2) + 3*a(n+1) - a(n) = 16.
E.g.f.: (1/3)*(3 + 6*x + 18*x^2 + 8*x^3)*exp(x). - G. C. Greubel, Jul 26 2016
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MATHEMATICA
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Table[1-2*n^2+4*n*(1+2*n^2)/3, {n, 0, 50}] (* G. C. Greubel, Jul 26 2016 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 3, 17, 59}, 60] (* Harvey P. Dale, May 21 2023 *)
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PROG
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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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