A227181 Irregular table: integers from n to n^2 followed by integers from (n+1) to (n+1)^2.

0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36

Offset: 0

Author

Antti Karttunen, Jul 03 2013

Keywords

• nonn
• tabf

Examples

			Row n is A002061(n) terms long, and contains successive integers from n to n*n:
  0;
  1;
  2, 3, 4;
  3, 4, 5, 6, 7, 8, 9;
  4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16;
  ...
		

Links

• Antti Karttunen, Rows 0..31, flattened

Crossrefs

Right edge: A000290. Central diagonal: A000217. Cf. also A227147.

Programs

Mathematica

Flatten[(#+Range[(#1-2) (#1-1)+1]-2&)[Range[7]]] (* Peter J. C. Moses, Jul 11 2013 *)
Table[Range[n,n^2],{n,0,6}]//Flatten (* Harvey P. Dale, Apr 03 2021 *)

Python

from sympy import integer_nthroot
def A227181(n): return n-(r:=(m:=integer_nthroot(k:=3*n,3)[0])-(k<=m*(m**2+2)))*(r**2-1)//3 # Chai Wah Wu, Nov 07 2024

Scheme

(define (A227181 n) (+ (A227177 n) (A227179 n)))

Formula

a(n) = A227177(n)+ A227179(n). [As a sequence].