A159798 Triangle read by rows in which row n lists n terms, starting with 1, such that the difference between successive terms is equal to n-3.

1, 1, 0, 1, 1, 1, 1, 2, 3, 4, 1, 3, 5, 7, 9, 1, 4, 7, 10, 13, 16, 1, 5, 9, 13, 17, 21, 25, 1, 6, 11, 16, 21, 26, 31, 36, 1, 7, 13, 19, 25, 31, 37, 43, 49, 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 1, 11

Offset

1,8

Comments

Note that for n>1 the last term of the n-th row is the square A000290(n-2).

Row sums are n*(n^2-4*n+5)/2 = 1, 1, 3, 10, 25, 51, 91, 148, 225, ... - R. J. Mathar, Jul 17 2009, Jul 20 2009

Row sums are the positive terms of A162607. - Omar E. Pol, Jul 24 2009

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Formula

T(n,k) = 1 + k*(n-3), 0<=k<n. - R. J. Mathar, Jul 17 2009

Example

Triangle begins:
  1;
  1,  0;
  1,  1,  1;
  1,  2,  3,  4;
  1,  3,  5,  7,  9;
  1,  4,  7, 10, 13, 16;
  1,  5,  9, 13, 17, 21, 25;
  1,  6, 11, 16, 21, 26, 31, 36;
  1,  7, 13, 19, 25, 31, 37, 43, 49;
  1,  8, 15, 22, 29, 36, 43, 50, 57, 64;
  1,  9, 17, 25, 33, 41, 49, 57, 65, 73, 81;
  1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100;

Mathematica

Table[1 + k*(n-3), {n, 1, 20}, {k, 0, n-1}]// Flatten (* G. C. Greubel, Apr 21 2018 *)

Prog

(PARI) for(n=1, 20, for(k=0, n-1, print1(1 + k*(n-3), ", "))) \\ G. C. Greubel, Apr 21 2018
(Magma) /* As triangle */ [[1 + k*(n-3): k in [0..n-1]]: n in [1..15]]; // G. C. Greubel, Apr 21 2018

Crossrefs

Cf. A000290, A081493, A159797, A162607, A162609, A162610, A162611.

Sequence in context: A141063 A138223 A194742 * A294236 A280694 A270313

Adjacent sequences: A159795 A159796 A159797 * A159799 A159800 A159801

Keyword

easy,nonn,tabl

Author

Omar E. Pol, Jul 09 2009

Extensions

More terms from R. J. Mathar, Jul 17 2009

Typo in row sums corrected by R. J. Mathar, Jul 20 2009

Edited by Omar E. Pol, Jul 24 2009

Status

approved