A101037 Triangle read by rows: T(n,1) = T(n,n) = n and for 1

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, 8, 6, 4, 2, 2, 4, 6, 8, 9, 7, 5, 3, 2, 3, 5, 7, 9, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 13, 11, 9, 7, 5, 3, 2, 3, 5, 7, 9, 11, 13, 14, 12, 10, 8, 6, 4, 2, 2, 4, 6, 8, 10, 12, 14

Offset: 1

Author

Reinhard Zumkeller, Nov 27 2004

Keywords

• nonn
• tabl

Comments

For n>1: sum of n-th row = A007590(n+1).

Examples

			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;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

Programs

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 *)

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)