A288690 Number of n-digit biquanimous strings using digits {0,1,...,6}.

1, 1, 7, 64, 633, 5801, 48245, 372345, 2743793, 19706380, 139666975, 983424751, 6902981425, 48383824035, 338898209049, 2373012819041, 16613639684833, 116304663546706, 814166474511867, 5699292259116239, 39895529322328145, 279270568611716769, 1954901225698086549

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 (35, -557, 5373, -35284, 167758, -599018, 1643178, -3510009, 5878447, -7726457, 7932089, -6287970, 3771376, -1654048, 500240, -93216, 8064).

Crossrefs

Column k=6 of A288638.

Formula

G.f.: -(4032*x^20 -50640*x^19 +300760*x^18 -1131816*x^17 +2828844*x^16 -5169218*x^15 +7372355*x^14 -8685305*x^13 +8984178*x^12 -8471674*x^11 +7172188*x^10 -5192457*x^9 +3073627*x^8 -1446472*x^7 +532167*x^6 -150791*x^5 +32203*x^4 -4997*x^3 +529*x^2 -34*x +1) / ((7*x-1) *(4*x-1) *(3*x-1)^2 *(2*x-1)^5 *(x-1)^8).