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 1-6 of 6 results.

A269061 Magic sums of 3 X 3 semimagic squares composed of positive squares.

Original entry on oeis.org

3249, 3969, 5041, 5691, 6241, 6561, 7329, 8281, 8649, 8841, 9025, 9801, 10011, 10794, 11025, 11306, 11449, 11881, 12219, 12321, 12769, 12996, 13689, 13699, 13701, 14114, 14161, 14641, 15129, 15876, 16129, 16186, 16625, 16641, 17059, 17081, 17161, 17689
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 18 2016

Keywords

Examples

			A semimagic square with sum 3249:
  |----|----|----|
  | 16 | 529|2704|
  |----|----|----|
  |1024|1936| 289|
  |----|----|----|
  |2209| 784| 256|
  |----|----|----|

Links

Crossrefs

Subsequence of A265198 and A269062.
Cf. A000290, A265141, A269060.

A265141 Irregular table read by rows: n-th row lists the 9 n-gonal numbers of a 3 X 3 semimagic square with the smallest magic sum. The terms of each row are arranged in the manner shown in A261816.

Original entry on oeis.org

15, 66, 630, 231, 435, 45, 465, 210, 36, 16, 529, 2704, 1024, 1936, 289, 2209, 784, 256, 651, 54626, 356972, 135751, 241001, 35497, 275847, 116622, 19780, 6, 39621, 481671, 158766, 345696, 16836, 362526, 135981, 22791, 697, 93799, 662290, 298771, 448804, 9211, 457318, 214183, 85285
Offset: 3

Views

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

Comments

The squares presented in this sequence are basic semimagic. For a definition of basic semimagic squares, see A261816.
The magic constants are, respectively: 711 = A269060(1), 3249 = 57^2 = A269061(1), and 412249.

Examples

			The semimagic squares are:
triangular numbers
|---|---|---|
| 15| 66|630|
|---|---|---|
|231|435| 45|
|---|---|---|
|465|210| 36|
|---|---|---|
.
square numbers
|----|----|----|
| 16 | 529|2704|
|----|----|----|
|1024|1936| 289|
|----|----|----|
|2209| 784| 256|
|----|----|----|
.
pentagonal numbers
|------|------|------|
|  651 | 54626|356972|
|------|------|------|
|135751|241001| 35497|
|------|------|------|
|275847|116622| 19780|
|------|------|------|

Links

Crossrefs

Cf. A269060, A269061, A265142.

Extensions

More terms from Arkadiusz Wesolowski, Apr 03 2016

A271020 Magic sums of 3 X 3 semimagic squares of triangular numbers whose rows, columns, and at least one of the two main diagonals sum to the same number.

Original entry on oeis.org

49288842, 62620221, 116153046, 128221941, 132479727, 443599581, 563581992, 750128651, 1045377417, 1153997472, 1192317546, 1232221059, 1565505534, 1881096741, 2192812511, 2415153276, 2903826159, 3068390847, 3205548534, 3311993184, 3647394275, 3992396232
Offset: 1

Views

Author

Arkadiusz Wesolowski, Mar 28 2016

Keywords

Links

Crossrefs

Cf. A271021, A271022. Subsequence of A269060.

A265197 Magic sums of 3 X 3 semimagic squares composed of triangular numbers.

Original entry on oeis.org

711, 1251, 1527, 1712, 2132, 2486, 2616, 2812, 2934, 3357, 3441, 3781, 3812, 4156, 4288, 4842, 4971, 4972, 5034, 5346, 5382, 5659, 5842, 5886, 6147, 6159, 6402, 6734, 6747, 7062, 7312, 7403, 7592, 7722, 8034, 8102, 8342, 8831, 8862, 8961, 9092, 9117
Offset: 1

Views

Author

Arkadiusz Wesolowski, Dec 04 2015

Keywords

Comments

These semimagic squares are composed of 9 distinct triangular numbers >= 0.

Examples

			A semimagic square with sum 1527:
  |----|----|----|
  | 0  |351 |1176|
  |----|----|----|
  |666 |741 |120 |
  |----|----|----|
  |861 |435 |231 |
  |----|----|----|

Links

Crossrefs

Cf. A000217, A265141, A265198, A269060 (for positive triangular numbers).

A269062 Magic sums of 3 X 3 semimagic squares composed of positive triangular numbers and squares.

Original entry on oeis.org

136, 146, 161, 175, 200, 230, 236, 250, 263, 277, 280, 290, 301, 316, 317, 326, 340, 346, 355, 370, 382, 394, 395, 398, 406, 410, 416, 421, 425, 431, 434, 436, 445, 446, 450, 461, 470, 472, 481, 484, 487, 494, 497, 499, 502, 511, 515, 518, 520, 527, 530
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 18 2016

Keywords

Examples

			A semimagic square with sum 136:
  |----|----|----|
  |  6 | 25 |105 |
  |----|----|----|
  | 49 | 66 | 21 |
  |----|----|----|
  | 81 | 45 | 10 |
  |----|----|----|

Links

Crossrefs

Cf. A269060, A269061.

A265142 a(n) = smallest magic sum of any 3 X 3 semimagic square composed of n-gonal numbers.

Original entry on oeis.org

711, 3249, 412249, 521298, 756786, 1076461
Offset: 3

Views

Author

Arkadiusz Wesolowski, Dec 02 2015

Keywords

Links

Crossrefs

Cf. A269060, A269061, A265141.

Formula

a(n) = Sum_{k=1..3} A265141(n,k).

Extensions

a(6)-a(8) from Arkadiusz Wesolowski, Apr 03 2016
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.