A080817 -id:A080817 - cp's OEIS frontend

A080819 Row sums from triangle in A080818.

1, 4, 9, 16, 16, 25, 36, 36, 49, 64, 81, 81, 100, 121, 121, 144, 169, 196, 196, 225, 256, 256, 289, 324, 361, 361, 400, 441, 441, 484, 529, 529, 576, 625, 676, 676, 729, 784, 784, 841, 900, 961, 961, 1024, 1089, 1089, 1156, 1225, 1225, 1296, 1369, 1444, 1444

Offset: 1

Amarnath Murthy, Mar 21 2003

nonn

Cf. A080817, A080818, A080820.

seq((ceil(sqrt(n*(n+1)/2)))^2,n=1..60); # C. Ronaldo

a(n) = (ceiling(sqrt(n*(n+1)/2)))^2. - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

A080820 Least m such that m^2 >= n*(n+1)/2.

Original entry on oeis.org

1, 2, 3, 4, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 38, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 45, 46, 47, 48, 48, 49, 50, 50, 51, 52, 52

Offset: 1

Amarnath Murthy, Mar 21 2003

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A080817, A080818, A080819.

seq(ceil(sqrt(n*(n+1)/2)),n=1..80); # C. Ronaldo

lst = {}; m = 1; Do[While[n*(n + 1)/2 > m^2, m++]; AppendTo[lst, m], {n, 69}]; lst (* Arkadiusz Wesolowski, Jul 18 2012 *)
Ceiling[Sqrt[#]]&/@Accumulate[Range[80]] (* Harvey P. Dale, Feb 10 2016 *)

a(n) = A080819(n)^(1/2).

a(n) = ceiling(sqrt(n*(n+1)/2)) - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

Name changed by Arkadiusz Wesolowski, Jul 18 2012

A080818 Triangle read by rows in which the n-th row contains n distinct numbers whose sum is the smallest square.

Original entry on oeis.org

1, 1, 3, 1, 2, 6, 1, 2, 3, 10, 1, 2, 3, 4, 6, 1, 2, 3, 4, 5, 10, 1, 2, 3, 4, 5, 6, 15, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 22, 1, 2, 3, 4, 5, 6, 7, 8

Offset: 1

Amarnath Murthy, Mar 21 2003

If n(n+1)/2 is a square triangular number then the n-th row contains first n natural numbers (e.g., the 8th row).

			1; 1,3; 1,2,6; 1,2,3,10; 1,2,3,4,6; 1,2,3,4,5,10; 1,2,3,4,5,6,15; 1,2,3,4,5,6,...

Cf. A080817, A080819, A080820.

seq(op([seq(i,i=1..n-1),(ceil(sqrt(n*(n+1)/2)))^2 - n*(n-1)/2]),n=1..15); # C. Ronaldo

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004

cp's OEIS Frontend

A080819 Row sums from triangle in A080818.

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A080820 Least m such that m^2 >= n*(n+1)/2.

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A080818 Triangle read by rows in which the n-th row contains n distinct numbers whose sum is the smallest square.

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