A141662 Triangle read by rows, T(n,m) = abs(n - m^2).

0, 1, 0, 2, 1, 2, 3, 2, 1, 6, 4, 3, 0, 5, 12, 5, 4, 1, 4, 11, 20, 6, 5, 2, 3, 10, 19, 30, 7, 6, 3, 2, 9, 18, 29, 42, 8, 7, 4, 1, 8, 17, 28, 41, 56, 9, 8, 5, 0, 7, 16, 27, 40, 55, 72, 10, 9, 6, 1, 6, 15, 26, 39, 54, 71, 90

Offset

0,4

Comments

Row sums are {0, 1, 5, 12, 24, 45, 75, 116, 170, 239, 327, ...}.

For n >= 1, the last number in row n is A002378(n-1).

Links

G. C. Greubel, Rows n = 0..100 of triangle, flattened

Formula

t(n,m) = abs(n - m^2).

Example

Triangle begins
  { 0},
  { 1,  0},
  { 2,  1,  2},
  { 3,  2,  1,  6},
  { 4,  3,  0,  5, 12},
  { 5,  4,  1,  4, 11, 20},
  { 6,  5,  2,  3, 10, 19, 30},
  { 7,  6,  3,  2,  9, 18, 29, 42},
  { 8,  7,  4,  1,  8, 17, 28, 41, 56},
  { 9,  8,  5,  0,  7, 16, 27, 40, 55, 72},
  {10,  9,  6,  1,  6, 15, 26, 39, 54, 71, 90}

Mathematica

T[n_, m_] = Abs[n - m^2]; Table[T[n, m], {n, 0, 10}, {m, 0, n}] // Flatten]

Prog

(PARI) for(n=0, 10, for(m=0, n, print1(abs(n - m^2), ", "))) \\ G. C. Greubel, Jun 08 2018

Crossrefs

Cf. A002378.

Sequence in context: A328266 A359895 A115116 * A328383 A088062 A248886

Adjacent sequences: A141659 A141660 A141661 * A141663 A141664 A141665

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Sep 05 2008

Extensions

Edited by N. J. A. Sloane, Jan 06 2009

Status

approved