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A165563
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a(n) = 1 + 2*n + n^2 + 2*n^3 + n^4.
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4
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1, 7, 41, 151, 409, 911, 1777, 3151, 5201, 8119, 12121, 17447, 24361, 33151, 44129, 57631, 74017, 93671, 117001, 144439, 176441, 213487, 256081, 304751, 360049, 422551, 492857, 571591, 659401, 756959, 864961, 984127, 1115201, 1258951, 1416169, 1587671
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OFFSET
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0,2
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COMMENTS
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Also binomial transform of the quasi-finite sequence 1,6,28,48,24,0 (0 continued).
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LINKS
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FORMULA
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a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24 -> 4th differences are 24 = A010863(n).
G.f.: (-1 - 2*x - 16*x^2 - 6*x^3 + x^4)/(x-1)^5.
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MATHEMATICA
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Table[1+2n+n^2+2n^3+n^4, {n, 0, 50}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {1, 7, 41, 151, 409}, 50] (* Harvey P. Dale, Nov 13 2021 *)
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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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