A288692 Number of n-digit biquanimous strings using digits {0,1,...,8}.

1, 1, 9, 109, 1457, 18231, 205837, 2112384, 20341201, 189013501, 1725377947, 15622028115, 140950202021, 1269874954518, 11433967343409, 102926130336136, 926421241593985, 8338171770377449, 75045297684511343, 675415983886759045, 6078784024809901485

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 (49, -1114, 15704, -154592, 1133720, -6448172, 29219972, -107498498, 325391618, -818066864, 1719218324, -3031985264, 4494756128, -5598534740, 5843651372, -5085390293, 3660194213, -2153194198, 1017730084, -376961752, 105342192, -20876832, 2614464, -155520).

Crossrefs

Column k=8 of A288638.

Formula

G.f.: -(77760*x^29 -1384992*x^28 [phone]*x^27 -69723432*x^26 [phone]*x^25 -975139270*x^24 [phone]*x^23 -5484438559*x^22 [phone]*x^21 -13997308104*x^20 [phone]*x^19 -18674789778*x^18 [phone]*x^17 -15836546206*x^16 [phone]*x^15 -9166750277*x^14 [phone]*x^13 -3404858524*x^12 [phone]*x^11 -773011544*x^10 [phone]*x^9 -97814317*x^8 [phone]*x^7 -5929660*x^6 +1052200*x^5 -145030*x^4 +14922*x^3 -1074*x^2 +48*x -1) / ((9*x-1) *(5*x-1) *(3*x-1)^3 *(2*x-1)^7 *(x-1)^12).