

A273751


Triangle of the natural numbers written by decreasing antidiagonals.


2



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, 24, 28, 33, 38, 44, 50, 57, 25, 29, 34, 39, 45, 51, 58, 65, 73, 30, 35, 40, 46, 52, 59, 66, 74, 82, 91, 36, 41
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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)*(x1)^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

Table of n, a(n) for n=1..57.
Wikipedia, Atomic orbital
Index entries for sequences that are permutations of the natural numbers


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 = n1 then
procname(n1, k)+k ;
else
procname(n1, k+1)+1 ;
end if;
end proc: # R. J. Mathar, Jun 13 2016


MATHEMATICA

T[n_, k_] := T[n, k] = Which[k == n, n(n1) + 1, k == n1, (n1)^2 + 1, k == 1, n + T[n2, 1], 1 < k < n1, T[n1, k+1] + 1, True, 0];
Table[T[n, k], {n, 12}, {k, n}] // Flatten (* JeanFrançois Alcover, Jun 10 2016 *)


CROSSREFS

Cf. A002061 (right diagonal), A002620 (first column), A033638, A091995, A234305 (antidiagonals of the triangle).
Sequence in context: A247714 A283734 A293052 * A056017 A091995 A343150
Adjacent sequences: A273748 A273749 A273750 * A273752 A273753 A273754


KEYWORD

nonn


AUTHOR

Paul Curtz, May 30 2016


STATUS

approved



