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

3,1

Comments

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

Links

Table of n, a(n) for n=3..50.

Eric Weisstein's World of Mathematics, Polygonal Number

Index entries for sequences related to magic squares

Example

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

Crossrefs

Cf. A271579, A271580, A271712.

Sequence in context: A215657 A157631 A085503 * A138843 A033386 A008896

Adjacent sequences: A271708 A271709 A271710 * A271712 A271713 A271714

Keyword

nonn,tabf

Author

Arkadiusz Wesolowski, Apr 12 2016

Status

approved