A386206 Triangle read by rows: T(n,k) = n^2 - k, with 0 <= k <= n.

0, 1, 0, 4, 3, 2, 9, 8, 7, 6, 16, 15, 14, 13, 12, 25, 24, 23, 22, 21, 20, 36, 35, 34, 33, 32, 31, 30, 49, 48, 47, 46, 45, 44, 43, 42, 64, 63, 62, 61, 60, 59, 58, 57, 56, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90

Offset

0,4

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3320 (rows 0..80)

Formula

G.f.: x*(1 + x + 2*x*y^2 + 5*x^3*y^2 - x^2*y*(4 + 5*y))/((1 - x)^3*(1 - x*y)^3).

T(n,1) = A005563(n-1) for n > 0.

T(n,2) = A008865(n) for n > 1.

Example

The triangle begins as:
   0;
   1,  0;
   4,  3,  2;
   9,  8,  7,  6;
  16, 15, 14, 13, 12;
  25, 24, 23, 22, 21, 20;
  36, 35, 34, 33, 32, 31, 30;
  49, 48, 47, 46, 45, 44, 43, 42;
  64, 63, 62, 61, 60, 59, 58, 57, 56;
  ...

Mathematica

T[n_, k_]:=n^2-k; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma) [[n^2-k: k in [0..n]]: n in [0..9]]; // Vincenzo Librandi, Jul 17 2025

Crossrefs

Cf. A000290 (k=0), A002414 (row sums), A005563, A008865, A028347 (k=4), A028872 (k=3), A028875 (k=5), A279019 (diagonal).

Sequence in context: A292828 A388524 A020703 * A084483 A266150 A276612

Adjacent sequences: A386203 A386204 A386205 * A386207 A386208 A386209

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Jul 15 2025

Status

approved