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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.

%I A265141 #46 Feb 16 2025 08:33:27
%S A265141 15,66,630,231,435,45,465,210,36,16,529,2704,1024,1936,289,2209,784,
%T A265141 256,651,54626,356972,135751,241001,35497,275847,116622,19780,6,39621,
%U A265141 481671,158766,345696,16836,362526,135981,22791,697,93799,662290,298771,448804,9211,457318,214183,85285
%N 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.
%C A265141 The squares presented in this sequence are basic semimagic. For a definition of basic semimagic squares, see A261816.
%C A265141 The magic constants are, respectively: 711 = A269060(1), 3249 = 57^2 = A269061(1), and 412249.
%H A265141 Arkadiusz Wesolowski, <a href="/A265141/b265141.txt">Rows n = 3..8, flattened</a>
%H A265141 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%H A265141 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A265141 The semimagic squares are:
%e A265141 triangular numbers
%e A265141 |---|---|---|
%e A265141 | 15| 66|630|
%e A265141 |---|---|---|
%e A265141 |231|435| 45|
%e A265141 |---|---|---|
%e A265141 |465|210| 36|
%e A265141 |---|---|---|
%e A265141 .
%e A265141 square numbers
%e A265141 |----|----|----|
%e A265141 | 16 | 529|2704|
%e A265141 |----|----|----|
%e A265141 |1024|1936| 289|
%e A265141 |----|----|----|
%e A265141 |2209| 784| 256|
%e A265141 |----|----|----|
%e A265141 .
%e A265141 pentagonal numbers
%e A265141 |------|------|------|
%e A265141 |  651 | 54626|356972|
%e A265141 |------|------|------|
%e A265141 |135751|241001| 35497|
%e A265141 |------|------|------|
%e A265141 |275847|116622| 19780|
%e A265141 |------|------|------|
%Y A265141 Cf. A269060, A269061, A265142.
%K A265141 nonn,tabf
%O A265141 3,1
%A A265141 _Arkadiusz Wesolowski_, Dec 02 2015
%E A265141 More terms from _Arkadiusz Wesolowski_, Apr 03 2016