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A083487
Triangle read by rows: T(n,k) = 2*n*k + n + k (1 <= k <= n).
9
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
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