OFFSET
1,2
COMMENTS
For n>1: sum of n-th row = A007590(n+1).
LINKS
Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)
FORMULA
From Robert Israel, Jan 30 2018: (Start)
T(n,k) = n - 2*k + 2 if k < (n+1)/2.
T(n,(n+1)/2) = 2 if n>1 is odd.
T(n,k) = 2*k - n if k > (n+1)/2.
G.f. as triangle: x*y*(x^6*y^3-2*x^5*y^3-2*x^5*y^2+x^4*y^3+3*x^4*y^2+x^4*y-3*x^2*y+1)/((1-x^2*y)*(1-x)^2*(1-x*y)^2).
(End)
EXAMPLE
Triangle begins:
1;
2, 2;
3, 2, 3;
4, 2, 2, 4;
5, 3, 2, 3, 5;
6, 4, 2, 2, 4, 6;
7, 5, 3, 2, 3, 5, 7;
...
MAPLE
T:= proc(n, k) if k < (n+1)/2 then n-2*k+2 elif k=(n+1)/2 then 2 else 2*k-n fi end proc:
T(1, 1):= 1:
seq(seq(T(n, k), k=1..n), n=1..20); # Robert Israel, Jan 30 2018
MATHEMATICA
T[n_, 1] := n; T[n_, n_] := n; T[n_, k_] := T[n, k] = Which[k < (n + 1)/2, n - 2*k + 2, k == (n + 1)/2, 2, True, 2*k - n];
Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 04 2019 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Nov 27 2004
STATUS
approved