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.

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

3,1

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.

Links

Arkadiusz Wesolowski, Rows n = 3..8, flattened

Eric Weisstein's World of Mathematics, Polygonal Number

Index entries for sequences related to magic squares

Example

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|
|------|------|------|

Crossrefs

Cf. A269060, A269061, A265142.

Sequence in context: A088058 A062392 A211787 * A336624 A211917 A015876

Adjacent sequences: A265138 A265139 A265140 * A265142 A265143 A265144

Keyword

nonn,tabf

Author

Arkadiusz Wesolowski, Dec 02 2015

Extensions

More terms from Arkadiusz Wesolowski, Apr 03 2016

Status

approved