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

1,2

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).

Formula

G.f.: (2764800*x^35 -54743040*x^34 +535723776*x^33 -3484062592*x^32 +17047244288*x^31 -67056352000*x^30 +220043616032*x^29 -610136398384*x^28 +1428398369904*x^27 -2800237309450*x^26 +4555415187081*x^25 -6116515610358*x^24 +6790044899737*x^23 -6333177380214*x^22 +5196278284089*x^21 -4097957831766*x^20 +3395084470412*x^19 -2936902021347*x^18 +2431358755383*x^17 -1791957130479*x^16 +1141680065910*x^15 -626654334304*x^14 +298277671441*x^13 -124021600362*x^12 +45181016933*x^11 -14371192060*x^10 +3953830871*x^9 -928344574*x^8 +183129613*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

Crossrefs

Cf. A064544, A065023, A065025, A065086.

Column k=9 of A288638.

Sequence in context: A240654 A128862 A129803 * A026244 A371405 A261503

Adjacent sequences: A065021 A065022 A065023 * A065025 A065026 A065027

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Nov 03 2001

Status

approved