cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A080819 Row sums from triangle in A080818.

Original entry on oeis.org

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

Views

Author

Amarnath Murthy, Mar 21 2003

Keywords

Crossrefs

Cf. A080817, A080818, A080820.

Programs

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

Formula

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

Extensions

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

A080817 Leading diagonal of triangle in A080818.

Original entry on oeis.org

1, 3, 6, 10, 6, 10, 15, 8, 13, 19, 26, 15, 22, 30, 16, 24, 33, 43, 25, 35, 46, 25, 36, 48, 61, 36, 49, 63, 35, 49, 64, 33, 48, 64, 81, 46, 63, 81, 43, 61, 80, 100, 58, 78, 99, 54, 75, 97, 49, 71, 94, 118, 66, 90, 115, 60, 85, 111, 138, 79, 106, 134, 72, 100, 129, 159, 93, 123
Offset: 1

Views

Author

Amarnath Murthy, Mar 21 2003

Keywords

Crossrefs

Cf. A080818, A080819, A080820.

Formula

From David Wasserman, May 13 2004: (Start)
a(n) = (ceiling(sqrt(n(n+1)/2)))^2 - n(n-1)/2.
a(n) = A048761(A000217(n)) - A000217(n-1). (End)

Extensions

More terms from David Wasserman, May 13 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

Views

Author

Amarnath Murthy, Mar 21 2003

Keywords

Links

Crossrefs

Cf. A080817, A080818, A080819.

Programs

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

Formula

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

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
Name changed by Arkadiusz Wesolowski, Jul 18 2012
Showing 1-3 of 3 results.

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