A271711 Irregular table read by rows: n-th row lists the 16 n-gonal numbers of a 4 X 4 magic square with the smallest magic sum, and the sum of the first two terms of each row is as small as it is possible.

66, 1, 300, 1035, 465, 630, 171, 136, 780, 105, 496, 21, 91, 666, 435, 210, 9, 1, 1444, 1369, 4, 2209, 169, 441, 1849, 324, 121, 529, 961, 289, 1089, 484, 115787, 24130, 1908012, 543305, 1214550, 1040417, 20475, 315792, 760060, 1526617, 3725, 300832, 500837, 70, 659022, 1431305

Offset: 3

Author

Arkadiusz Wesolowski, Apr 12 2016

Keywords

• nonn
• tabf

Comments

The magic constants are, respectively: 1402 = A271579(1), 2823 = A271580(1), and 2591234.

Examples

			The magic squares are:
triangular numbers
|----|----|----|----|
| 66 |  1 | 300|1035|
|----|----|----|----|
| 465| 630| 171| 136|
|----|----|----|----|
| 780| 105| 496| 21 |
|----|----|----|----|
| 91 | 666| 435| 210|
|----|----|----|----|
.
square numbers
|----|----|----|----|
|  9 |  1 |1444|1369|
|----|----|----|----|
|  4 |2209| 169| 441|
|----|----|----|----|
|1849| 324| 121| 529|
|----|----|----|----|
| 961| 289|1089| 484|
|----|----|----|----|
.
pentagonal numbers
|-------|-------|-------|-------|
| 115787| 24130 |1908012| 543305|
|-------|-------|-------|-------|
|1214550|1040417| 20475 | 315792|
|-------|-------|-------|-------|
| 760060|1526617|  3725 | 300832|
|-------|-------|-------|-------|
| 500837|   70  | 659022|1431305|
|-------|-------|-------|-------|
		

Links

• Eric Weisstein's World of Mathematics, Polygonal Number
• Index entries for sequences related to magic squares

Crossrefs

Cf. A271579, A271580, A271712.