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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.

%I A271711 #9 Feb 16 2025 08:33:33
%S A271711 66,1,300,1035,465,630,171,136,780,105,496,21,91,666,435,210,9,1,1444,
%T A271711 1369,4,2209,169,441,1849,324,121,529,961,289,1089,484,115787,24130,
%U A271711 1908012,543305,1214550,1040417,20475,315792,760060,1526617,3725,300832,500837,70,659022,1431305
%N 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.
%C A271711 The magic constants are, respectively: 1402 = A271579(1), 2823 = A271580(1), and 2591234.
%H A271711 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%H A271711 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A271711 The magic squares are:
%e A271711 triangular numbers
%e A271711 |----|----|----|----|
%e A271711 | 66 |  1 | 300|1035|
%e A271711 |----|----|----|----|
%e A271711 | 465| 630| 171| 136|
%e A271711 |----|----|----|----|
%e A271711 | 780| 105| 496| 21 |
%e A271711 |----|----|----|----|
%e A271711 | 91 | 666| 435| 210|
%e A271711 |----|----|----|----|
%e A271711 .
%e A271711 square numbers
%e A271711 |----|----|----|----|
%e A271711 |  9 |  1 |1444|1369|
%e A271711 |----|----|----|----|
%e A271711 |  4 |2209| 169| 441|
%e A271711 |----|----|----|----|
%e A271711 |1849| 324| 121| 529|
%e A271711 |----|----|----|----|
%e A271711 | 961| 289|1089| 484|
%e A271711 |----|----|----|----|
%e A271711 .
%e A271711 pentagonal numbers
%e A271711 |-------|-------|-------|-------|
%e A271711 | 115787| 24130 |1908012| 543305|
%e A271711 |-------|-------|-------|-------|
%e A271711 |1214550|1040417| 20475 | 315792|
%e A271711 |-------|-------|-------|-------|
%e A271711 | 760060|1526617|  3725 | 300832|
%e A271711 |-------|-------|-------|-------|
%e A271711 | 500837|   70  | 659022|1431305|
%e A271711 |-------|-------|-------|-------|
%Y A271711 Cf. A271579, A271580, A271712.
%K A271711 nonn,tabf
%O A271711 3,1
%A A271711 _Arkadiusz Wesolowski_, Apr 12 2016