A083487 Triangle read by rows: T(n,k) = 2*n*k + n + k (1 <= k <= n).

4, 7, 12, 10, 17, 24, 13, 22, 31, 40, 16, 27, 38, 49, 60, 19, 32, 45, 58, 71, 84, 22, 37, 52, 67, 82, 97, 112, 25, 42, 59, 76, 93, 110, 127, 144, 28, 47, 66, 85, 104, 123, 142, 161, 180, 31, 52, 73, 94, 115, 136, 157, 178, 199, 220, 34, 57, 80, 103, 126, 149, 172, 195, 218, 241, 264

Offset

1,1

Comments

T(n,k) gives number of edges (of unit length) in a k X n grid.

The values 2*T(n,k)+1 = (2*n+1)*(2*k+1) are nonprime and therefore in A047845.

Links

Vincenzo Librandi, Rows n = 1..100, flattened

Alain Kraus, Cours-Arithmétique et algèbre, 2016-2017, Université de Paris VI. See Exercice 6 p. 13.

OEIS Wiki, Odd composites

Formula

From G. C. Greubel, Oct 17 2023: (Start)

T(n, 1) = A016777(n).

T(n, 2) = A016873(n).

T(n, 3) = A017017(n).

T(n, 4) = A017209(n).

T(n, 5) = A017449(n).

T(n, 6) = A186113(n).

T(n, n-1) = A056220(n).

T(n, n-2) = A090288(n-2).

T(n, n-3) = A271625(n-2).

T(n, n) = 4*A000217(n).

T(2*n, n) = A033954(n).

Sum_{k=1..n} T(n, k) = A162254(n).

Sum_{k=1..n} (-1)^(k-1)*T(n, k) = A182868((n+1)/2) if n is odd otherwise A182868(n/2) + 1. (End)

Example

Triangle begins:
   4;
   7, 12;
  10, 17, 24;
  13, 22, 31, 40;
  16, 27, 38, 49,  60;
  19, 32, 45, 58,  71,  84;
  22, 37, 52, 67,  82,  97, 112;
  25, 42, 59, 76,  93, 110, 127, 144;
  28, 47, 66, 85, 104, 123, 142, 161, 180;

Mathematica

T[n_, k_]:= 2 n k + n + k; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* Vincenzo Librandi, Jun 01 2014 *)

Prog

(Magma) [(2*n*k + n + k): k in [1..n], n in [1..11]]; // Vincenzo Librandi, Jun 01 2014
(Python)
def T(r, c): return 2*r*c + r + c
a = [T(r, c) for r in range(12) for c in range(1, r+1)]
print(a) # Michael S. Branicky, Sep 07 2022
(SageMath) flatten([[2*n*k +n +k for k in range(1, n+1)] for n in range(1, 14)]) # G. C. Greubel, Oct 17 2023

Crossrefs

Cf. A000217, A016777, A016873, A017017, A017209, A017449, A033954.

Cf. A056220, A082652, A083003, A090288, A182868, A186113, A271625.

See A151890 for another version.

Sequence in context: A178939 A072732 A270684 * A253129 A249918 A340244

Adjacent sequences: A083484 A083485 A083486 * A083488 A083489 A083490

Keyword

nonn,tabl

Author

Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Jun 09 2003

Extensions

Edited by N. J. A. Sloane, Jul 23 2009

Name edited by Michael S. Branicky, Sep 07 2022

Status

approved