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A240928
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Number of 8-digit positive integers in base n where the sum of the first k digits equals the sum of the last k digits.
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2
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35, 750, 6174, 31025, 114961, 346193, 896876, 2072694, 4379055, 8606312, 15936426, 28073487, 47400509, 77164915, 121695128, 186650684, 279308283, 408886194, 586909430, 827618109, 1148421417, 1570399589, 2118856324, 2823924050, 3721224455, 4852586700
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OFFSET
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2,1
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COMMENTS
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These integers are sometimes called balanced numbers.
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REFERENCES
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Cambridge Colleges Sixth Term Examination Papers (STEP) 2007, Paper I, Section A (Pure Mathematics), Nr. 1.
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LINKS
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FORMULA
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a(n) = n*(n-1)*(1208*n^5+151*n^4+291*n^3+116*n^2+88*n+60)/2520.
G.f.: x^2*(x^5+83*x^4+673*x^3+1154*x^2+470*x+35)/(x-1)^8. - Alois P. Heinz, Mar 24 2022
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MATHEMATICA
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Table[n(n-1)(1208n^5+151n^4+291n^3+116n^2+88n+60)/2520, {n, 2, 40}] (* Harvey P. Dale, Mar 18 2022 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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