A240928 -id:A240928 - cp's OEIS frontend

A240927 Positive integers with 2k digits (the first of which is not 0) where the sum of the first k digits equals the sum of the last k digits.

11, 22, 33, 44, 55, 66, 77, 88, 99, 1001, 1010, 1102, 1111, 1120, 1203, 1212, 1221, 1230, 1304, 1313, 1322, 1331, 1340, 1405, 1414, 1423, 1432, 1441, 1450, 1506, 1515, 1524, 1533, 1542, 1551, 1560, 1607, 1616, 1625, 1634, 1643, 1652, 1661, 1670, 1708, 1717

Offset: 1

Martin Renner, Aug 03 2014

These integers are sometimes called balanced numbers.

There are 9, 615, 50412, 4379055, 392406145, ... 2k-digit balanced numbers with k >= 1.

			1423 is a 4-digit balanced number, because the sum of the first 2 digits equals the sum of the last 2 digits: 1 + 4 = 2 + 3.

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

Harvey P. Dale, Table of n, a(n) for n = 1..624 (All terms through 9999)

Cf. A016061, A197083, A240928, A240929.

sfslQ[n_]:=Module[{id=IntegerDigits[n],len},len=Length[id]/2;Total[Take[ id,len]]==Total[Take[id,-len]]]; Select[Table[Range[10^n,10^(n+1)-1],{n,1,3,2}]// Flatten,sfslQ] (* Harvey P. Dale, Jun 24 2020 *)

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.

Original entry on oeis.org

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

Martin Renner, Aug 03 2014

These integers are sometimes called balanced numbers.

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

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

Cf. A016061, A197083, A240927, A240928.

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

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)

cp's OEIS Frontend

A240927 Positive integers with 2k digits (the first of which is not 0) where the sum of the first k digits equals the sum of the last k digits.

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