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A062159
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a(n) = n^5 - n^4 + n^3 - n^2 + n - 1.
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4
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-1, 0, 21, 182, 819, 2604, 6665, 14706, 29127, 53144, 90909, 147630, 229691, 344772, 501969, 711914, 986895, 1340976, 1790117, 2352294, 3047619, 3898460, 4929561, 6168162, 7644119, 9390024, 11441325, 13836446, 16616907, 19827444, 23516129, 27734490, 32537631, 37984352, 44137269
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listen;
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OFFSET
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0,3
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COMMENTS
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Number of walks of length 6 between any two distinct nodes of the complete graph K_{n+1} (n>=1). - Emeric Deutsch, Apr 01 2004
For odd n, a(n) * (n+1) / 2 + 1 also represents the first integer in a sum of n^6 consecutive integers that equals n^12. - Patrick J. McNab, Dec 26 2016
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LINKS
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FORMULA
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a(n) = round(n^6/(n+1)) for n>2 = A062160(n,6).
G.f.: (76x^3 + 6x^2 + 27x^4 + 6x^5 + 6x - 1)/(1-x)^6 (for the signed sequence). - Emeric Deutsch, Apr 01 2004
a(0)=-1, a(1)=0, a(2)=21, a(3)=182, a(4)=819, a(5)=2604, a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Harvey P. Dale, Dec 20 2015
E.g.f.: exp(x)*(x^5 + 9*x^4 + 20*x^3 + 10*x^2 + x - 1). - Stefano Spezia, Apr 22 2023
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EXAMPLE
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a(4) = 4^5 - 4^4 + 4^3 - 4^2 + 4 - 1 = 1024 - 256 + 64 - 16 + 4 - 1 = 819.
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MAPLE
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MATHEMATICA
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LinearRecurrence[{6, -15, 20, -15, 6, -1}, {-1, 0, 21, 182, 819, 2604}, 40] (* Harvey P. Dale, Dec 20 2015 *)
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PROG
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(PARI) { for (n=0, 1000, write("b062159.txt", n, " ", n*(n*(n*(n*(n - 1) + 1) - 1) + 1) - 1) ) } \\ Harry J. Smith, Aug 02 2009
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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