A288691 Number of n-digit biquanimous strings using digits {0,1,...,7}.

1, 1, 8, 85, 988, 10696, 104676, 939863, 7980376, 65679175, 532115106, 4279710436, 34311898336, 274729437763, 2198561705222, 17590732383423, 140732804110800, 1125884352801489, 9007145852828686, 72057404552774828, 576460059887430848, 4611683426113781209

Offset: 0

Author

Alois P. Heinz, Jun 13 2017

Keywords

• nonn
• easy

Comments

A biquanimous string is a string whose digits can be split into two groups with equal sums.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (40, -734, 8256, -64063, 365480, -1593840, 5449456, -14855999, 32647032, -58206694, 84416480, -99491505, 94840120, -72455660, 43708272, -20343280, 7044608, -1708352, 258816, -18432).

Crossrefs

Column k=7 of A288638.

Formula

G.f.: (9216*x^24 -129408*x^23+881824*x^22 -3910528*x^21 [phone]*x^20 -31636760*x^19 [phone]*x^18 -101187417*x^17 [phone]*x^16 -166854657*x^15 [phone]*x^14 -158809357*x^13 [phone]*x^12 -89880736*x^11 [phone]*x^10 -29668152*x^9 [phone]*x^8 -4887342*x^7 +1441132*x^6 -333899*x^5 +59267*x^4 -7757*x^3 +702*x^2 -39*x +1) / ((8*x-1) *(4*x-1) *(3*x-1)^2 *(2*x-1)^6 *(x-1)^10).