A080521 Triangle read by rows; n-th row contains the lexicographically first set of n distinct positive integers whose sum is 2^n.

2, 1, 3, 1, 2, 5, 1, 2, 3, 10, 1, 2, 3, 4, 22, 1, 2, 3, 4, 5, 49, 1, 2, 3, 4, 5, 6, 107, 1, 2, 3, 4, 5, 6, 7, 228, 1, 2, 3, 4, 5, 6, 7, 8, 476, 1, 2, 3, 4, 5, 6, 7, 8, 9, 979, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1993, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4030

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10011 (rows 1 to 141, flattened)

Formula

From Jon E. Schoenfield, Jul 30 2017: (Start)

T(n,k) = k for 1 <= k < n;

T(n,n) = 2^n - n(n-1)/2. (End)

G.f.: x*y*(2 - x - 7*x*y + 4*x^2*y + 8*x^2*y^2 - 6*x^3*y^2 - 2*x^3*y^3 + 2*x^4*y^3)/((1-x*y)^3*(1-x)*(1-2*x*y)). - Robert Israel, Jul 04 2019

Example

Triangle begins
  2;
  1,  3;
  1,  2,  5;
  1,  2,  3, 10;
  1,  2,  3,  4, 22;
  1,  2,  3,  4,  5, 49;

Maple

for n from 1 to 20 do
seq(k, k=1..n-1), 2^n-n*(n-1)/2
od; # Robert Israel, Jul 04 2019

Mathematica

Array[Join[Range[# - 1], {2^# - #*(# - 1)/2}] &, 15] // Flatten (* Paolo Xausa, Mar 16 2024 *)

Prog

(PARI) print(2, "; "); for(i=2, 20, s=0; for(j=1, i-1, print1(j, ", "); s+=j); print(2^i-s, "; ")) \\ Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jul 19 2005

Crossrefs

Cf. A080522.

First diagonal is A014844 (2^n - n(n-1)/2).

Sequence in context: A257918 A257912 A036262 * A169613 A176572 A168017

Adjacent sequences: A080518 A080519 A080520 * A080522 A080523 A080524

Keyword

nonn,tabl

Author

Amarnath Murthy, Mar 21 2003

Extensions

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jul 19 2005

T(1,1) = 2 inserted by Jon E. Schoenfield and Michel Marcus, Jul 30 2017

Status

approved