A123329 Let M be the matrix defined in A111490. Sequence gives M(2,1)-M(1,2), M(2,1)+M(3,1)+M(3,2)-M(1,2)-M(1,3)-M(2,3), etc.
0, 1, 3, 8, 14, 26, 39, 59, 83, 115, 148, 197, 247, 307, 376, 460, 545, 651, 758, 887, 1027, 1181, 1336, 1527, 1724, 1937, 2163, 2417, 2672, 2969, 3267, 3596, 3940, 4304, 4681, 5113, 5546, 6001, 6473, 6995, 7518, 8095, 8673, 9291, 9942, 10619, 11297, 12051
Offset: 0
Keywords
Links
- Ray Chandler, Table of n, a(n) for n = 0..10000 (corrected original b-file from Michael S. Branicky missing two terms at request of Christian Krause)
Crossrefs
Programs
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Maple
b:= proc(n) option remember; `if`(n=0, [0$2], (p-> p +[numtheory[sigma](n)-n$2]+[0, p[1]])(b(n-1))) end: a:= n-> b(n+1)[2]: seq(a(n), n=0..50); # Alois P. Heinz, Jan 21 2021
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Mathematica
b[n_] := b[n] = If[n == 0, {0, 0}, With[{p = b[n-1]}, p + DivisorSigma[1, n] - n + {0, p[[1]]}]]; a[n_] := b[n+1][[2]]; Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Jul 10 2021, after Alois P. Heinz *)
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Python
def M(n,k): return 1 + (k-1)%n def a(n): return sum(M(i,j)-M(j,i) for i in range(2, n+3) for j in range(1, i)) print([a(n) for n in range(48)]) # Michael S. Branicky, Jan 20 2021
Formula
a(n) = binomial(n+2,3) - A072481(n+1). - Robert Israel, Aug 13 2015
a(n) = Sum_{i=2..(n+2)} Sum_{j=1..i-1} (M(i,j)-M(j,i)). - Michael S. Branicky, Jan 20 2021
Extensions
a(14) and beyond from Michael S. Branicky, Jan 20 2021
Comments