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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. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 23:16 EST 2020. Contains 331104 sequences. (Running on oeis4.)