login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A065024
Number of n-digit biquanimous numbers in base 10 allowing leading zeros.
7
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
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
Column k=9 of A288638.
Sequence in context: A240654 A128862 A129803 * A026244 A371405 A261503
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, Nov 03 2001
STATUS
approved