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A255181
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Third differences of seventh powers (A001015).
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5
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1, 125, 1806, 10206, 35406, 92526, 201726, 388206, 682206, 1119006, 1738926, 2587326, 3714606, 5176206, 7032606, 9349326, 12196926, 15651006, 19792206, 24706206, 30483726, 37220526, 45017406, 53980206, 64219806, 75852126, 88998126, 103783806, 120340206
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listen;
history;
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (1 + 120*x + 1191*x^2 + 2416*x^3 + 1191*x^4 + 120*x^5 + x^6)/(1 - x)^5.
a(n) = 42*(3 - 10*n + 15*n^2 - 10*n^3 + 5*n^4) for n>1, a(0)=1, a(1)=125.
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EXAMPLE
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Third differences: 1, 125, 1806, 10206, 35406, ... (this sequence)
Second differences: 1, 126, 1932, 12138, 47544, ... (A255177)
First differences: 1, 127, 2059, 14197, 61741, ... (A022523)
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The seventh powers: 1, 128, 2187, 16384, 78125, ... (A001015)
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MATHEMATICA
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Join[{1, 125}, Table[42 (3 - 10 n + 15 n^2 - 10 n^3 + 5 n^4), {n, 2, 30}]]
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PROG
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(Magma) [1, 125] cat [42*(3-10*n+15*n^2-10*n^3+5*n^4): n in [2..30]]; // Vincenzo Librandi, Mar 18 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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EXTENSIONS
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STATUS
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approved
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