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A240928
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.
2
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
OFFSET
2,1
COMMENTS
These integers are sometimes called balanced numbers.
REFERENCES
Cambridge Colleges Sixth Term Examination Papers (STEP) 2007, Paper I, Section A (Pure Mathematics), Nr. 1.
FORMULA
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
MATHEMATICA
Table[n(n-1)(1208n^5+151n^4+291n^3+116n^2+88n+60)/2520, {n, 2, 40}] (* Harvey P. Dale, Mar 18 2022 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Martin Renner, Aug 03 2014
STATUS
approved