A240929 Number of 10-digit positive integers in base n where the sum of the first k digits equals the sum of the last k digits.

126, 6046, 88428, 694360, 3705741, 15192604, 51418473, 150420187, 392406145, 933294637, 2056947827, 4253047045, 8329101326, 15566783605, 27934647638, 48371293570, 81155221112, 132379936520, 210555362990, 327359243694, 498565022483, 745175639274, 1094795785319

Offset

2,1

Comments

These integers are sometimes called balanced numbers.

References

Cambridge Colleges Sixth Term Examination Papers (STEP) 2007, Paper I, Section A (Pure Mathematics), Nr. 1.

Links

Table of n, a(n) for n=2..24.

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = n*(n-1)*(156190*n^7 + 15619*n^6 + 45019*n^5 + 14149*n^4 + 18139*n^3 + 9760*n^2 + 6660*n + 5040)/362880

From Chai Wah Wu, May 08 2024: (Start)

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n > 11.

G.f.: x^2*(x^7 + 326*x^6 + 7942*x^5 + 42341*x^4 + 67030*x^3 + 33638*x^2 + 4786*x + 126)/(x - 1)^10. (End)

Prog

(Python)
def A240929(n): return n*(n*(n*(n*(n*(n*(n*(n*(156190*n-140571)+29400)-30870)+3990)-8379)-3100)-1620)-5040)//362880 # Chai Wah Wu, May 08 2024

Crossrefs

Cf. A016061, A197083, A240927, A240928.

Sequence in context: A140902 A270512 A037963 * A285172 A208618 A352334

Adjacent sequences: A240926 A240927 A240928 * A240930 A240931 A240932

Keyword

nonn,base,easy

Author

Martin Renner, Aug 03 2014

Status

approved