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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.
6
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
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
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
More terms from Arkadiusz Wesolowski, Apr 03 2016
STATUS
approved