A124797 -id:A124797 - cp's OEIS frontend

A124798 Sequence of digits (least significant digit first) of A124797 (sums of cyclic permutations of 1...n written in base n+1).

1, 0, 1, 1, 2, 3, 3, 1, 0, 2, 2, 2, 2, 3, 5, 5, 5, 5, 2, 0, 3, 3, 3, 3, 3, 3, 4, 7, 7, 7, 7, 7, 7, 3, 0, 4, 4, 4, 4, 4, 4, 4, 4, 5, 9, 9, 9, 9, 9, 9, 9, 9, 4, 0, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 5, 0, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 13, 13, 13, 13, 13, 13

Offset: 1

M. F. Hasler, Nov 07 2006

Sequence A083956 becomes "unnatural" for n>9. It is easily seen that for n=2k, the sum of permutations A124797(n) is {k:n}0 in base n+1 where {k:n} means n times the digit k; while for n=2k+1 (>1), the sum is k{n:2k}{k+1} (again in base n+1). In particular, this number has n+1 digits (for n>1), such that the digits for A124797(n) start at place n(n+1)/2-1 (for n>1).

			a(1)=1, the sum of cyclic permutations of 1;
a(2..4)=0,1,1 since 12 + 21 = 110 in base 3;
a(5..8)=2,3,3,1 since 123 + 231 + 312 = 1332 in base 4;
a(9..13)=0,2,2,2,2 since 1234 + 2341 + 3412 + 4123 = 22220 in base 5.

Cf. A083956, A124797.

A124797 := n->(n+1)/2*((n+1)^n-1): map(op, [ 'convert(A124797(i),base,i+1)' $ i=1..20 ]);

A214698 a(n) = (n^n - n^2)/2.

Original entry on oeis.org

0, 0, 9, 120, 1550, 23310, 411747, 8388576, 193710204, 4999999950, 142655835245, 4458050224056, 151437553296042, 5556003412778910, 218946945190429575, 9223372036854775680, 413620130943168381944, 19673204037648268787550, 989209827830156794561809, 52428799999999999999999800

Offset: 1

Alex Ratushnyak, Jul 26 2012

			a(3) = (27 - 9)/2 = 9.

Harvey P. Dale, Table of n, a(n) for n = 1..386

Cf. A124797 is essentially equal to (n^n-n)/2.

Cf. A000217, A117694, A214647.

[(n^n -n^2)/2: n in [1..30]]; // G. C. Greubel, Jan 08 2024

A214698:= proc(n)
    (n^n-n^2)/2 ;
end proc: # R. J. Mathar, Aug 07 2012

Table[(n^n-n^2)/2,{n,30}] (* Harvey P. Dale, Dec 25 2022 *)

for n in range(1, 22):
    print((n**n - n*n)//2)

[(n^n -n^2)/2 for n in range(1,31)] # G. C. Greubel, Jan 08 2024

a(n) = A214647(n) - n^2 = A117694(n) - A000217(n).

E.g.f.: (-1/2)*(lambertW(-x)/(1 + lambertW(-x)) + x*(x+1)*exp(x)). - G. C. Greubel, Jan 08 2024

cp's OEIS Frontend

A124798 Sequence of digits (least significant digit first) of A124797 (sums of cyclic permutations of 1...n written in base n+1).

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A214698 a(n) = (n^n - n^2)/2.

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