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.

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

Author

Martin Renner, Aug 03 2014

Keywords

• nonn
• base

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.

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A016061, A197083, A240927, A240929.

Programs

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 *)

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