OFFSET
1,2
COMMENTS
A permutation of the natural numbers.
a(n) and A091995(n) are different at the ninth term.
Antidiagonal sums: 1, 2, 7, 11, ... = A235355(n+1). Same idea.
Row sums: 1, 5, 16, 37, 72, 124, 197, 294, ... = 7*n^3/12 -n^2/8 +5*n/12 +1/16 -1/16*(-1)^n with g.f. x*(1+2*x+3*x^2+x^3) / ( (1+x)*(x-1)^4 ). The third difference is of period 2: repeat [3, 4].
Indicates the order in which electrons fill the different atomic orbitals (s,p,d,f,g,h). - Alexander Goebel, May 12 2020
LINKS
FORMULA
T(n, k) = (2 * (n+k)^2 + 7 + (-1)^(n-k)) / 8 - k. - Werner Schulte, Sep 27 2024.
EXAMPLE
1,
2, 3,
4, 5, 7,
6, 8, 10, 13,
9, 11, 14, 17, 21,
12, 15, 18, 22, 26, 31,
16, 19, 23, 27, 32, 37, 43,
20, etc.
MAPLE
A273751 := proc(n, k)
option remember;
if k = n then
A002061(n) ;
elif k > n or k < 0 then
0;
elif k = n-1 then
procname(n-1, k)+k ;
else
procname(n-1, k+1)+1 ;
end if;
end proc: # R. J. Mathar, Jun 13 2016
MATHEMATICA
T[n_, k_] := T[n, k] = Which[k == n, n(n-1) + 1, k == n-1, (n-1)^2 + 1, k == 1, n + T[n-2, 1], 1 < k < n-1, T[n-1, k+1] + 1, True, 0];
Table[T[n, k], {n, 12}, {k, n}] // Flatten (* Jean-François Alcover, Jun 10 2016 *)
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Paul Curtz, May 30 2016
STATUS
approved