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 1-2 of 2 results.

A341199 First differences of A341198.

Original entry on oeis.org

4, 16, 16, 24, 36, 32, 48, 44, 56, 72, 64, 76, 80, 88, 92, 96, 112, 116, 120, 120, 128, 140, 152, 144, 148, 184, 160, 184, 172, 184, 208, 188, 208, 208, 220, 240, 224, 240, 244, 256, 256, 252, 288, 272, 280, 276, 296, 312, 308, 320, 312, 328, 340, 328, 344
Offset: 1

Views

Author

Pontus von Brömssen, Feb 06 2021

Keywords

Crossrefs

Cf. A341198.

Formula

a(n) = A341198(n) - A341198(n-1).
a(n) == 0 (mod 4).
If A341198(n) = Pi*n^2 + c*n + o(n) for some constant c (as suggested in a comment to A341198), it holds that a(n) ~ 2*Pi*n + o(n).

A372847 Number of unit squares enclosed by a circle of radius n with an even number of rows and the maximum number of squares in each row.

Original entry on oeis.org

0, 6, 18, 36, 64, 92, 130, 172, 224, 284, 344, 410, 488, 570, 658, 750, 852, 956, 1072, 1194, 1312, 1450, 1584, 1728, 1882, 2044, 2204, 2372, 2548, 2730, 2916, 3112, 3312, 3520, 3738, 3950, 4184, 4408, 4656, 4900, 5146, 5402, 5670, 5942, 6222, 6492, 6784, 7080, 7382, 7700
Offset: 1

Views

Author

David Dewan, May 14 2024

Keywords

Comments

Always has an even number of rows (2*n-2) and each row may have an odd or even number of squares.
Symmetrical about the horizontal and vertical axes.

Examples

			For n=4
row 1:   5 squares
row 2:   6 squares
row 3:   7 squares
row 4:   7 squares
row 5:   6 squares
row 6:   5 squares
Total = 36

Links

Crossrefs

Cf. A136485 (by diameter), A001182 (within quadrant), A136483 (quadrant by diameter), A119677 (even number of rows with even number of squares in each), A125228 (odd number of rows with maximal squares per row), A341198 (points rather than squares).

Programs

  • Mathematica
    a[n_]:=2 Sum[Floor[2 Sqrt[n^2 - k^2]], {k,n-1}]; Array[a,50]

Formula

a(n) = 2*Sum_{k=1..n-1} floor(2*sqrt(n^2 - k^2)).
Showing 1-2 of 2 results.

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