A065024 Number of n-digit biquanimous numbers in base 10 allowing leading zeros.

1, 10, 136, 2056, 29246, 376414, 4366881, 47111408, 487875964, 4951921240, 49815780829, 499304300676, 4997363405880, 49989815235610, 499959437775564, 4999832460244272, 49999282163551040, 499996822399017380, 4999985554326500949, 49999932964605448756, 499999684083134646700, 4999998493912339729030, 49999992756990963293576, 499999964931001199898296, 4999999829289953917354596

Offset: 1

Author

N. J. A. Sloane, Nov 03 2001

Keywords

• nonn
• base
• easy

Comments

A biquanimous number (A064544) is a number whose digits can be split into two groups with equal sums.

References

• William P. Thurston, personal communication.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (62, -1807, 33062, -427564, 4169600, -31932484, 197416064, -1004816182, 4272066348, -15337434186, 46879240956, -122734147260, 276448013616, -537280650948, 902485024560, -1310712845937, 1644560278758, -1778909274239, 1653055768558, -1312795678832, 884596325632, -500792236832, 235030416448, -89771423744, 27185833984, -6278031104, 1038269952, -109486080, 5529600).

Crossrefs

Cf. A064544, A065023, A065025, A065086.

Column k=9 of A288638.

Formula

G.f.: (2764800*x^35 -54743040*x^34 [phone]*x^33 -3484062592*x^32 [phone]*x^31 -67056352000*x^30 [phone]*x^29 -610136398384*x^28 [phone]*x^27 -2800237309450*x^26 [phone]*x^25 -6116515610358*x^24 [phone]*x^23 -6333177380214*x^22 [phone]*x^21 -4097957831766*x^20 [phone]*x^19 -2936902021347*x^18 [phone]*x^17 -1791957130479*x^16 [phone]*x^15 -626654334304*x^14 [phone]*x^13 -124021600362*x^12 [phone]*x^11 -14371192060*x^10 [phone]*x^9 -928344574*x^8 [phone]*x^7 -29820446*x^6 +3925130*x^5 -406196*x^4 +31739*x^3 -1755*x^2 +61*x-1) / ((10*x-1) *(5*x-1) *(4*x-1)^2 *(3*x-1)^3 *(2*x-1)^8 *(x-1)^14). - Alois P. Heinz, Jun 12 2017

Limit_{n->oo} a(n)/10^n = 1/2. - Stefano Spezia, Sep 09 2023