有多少个周长为 n 、三边边长都是整数的三角形？

王守恩

周长为n, 有a(n)个3边为整数的3边形。
Table[Length@Select[IntegerPartitions[n, {3}], Max[#]2<n &], {n, 3, 100}]
{1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4,7, 5, 8, 7,10, 8, 12, 10, 14, 12, 16,14, 19, 16,21, 19, 24, 21, 27,  

周长为n, 有a(n)个4边为整数的4边形。
Table[Length@Select[IntegerPartitions[n, {4}], Max[#]2<n &], {n, 4, 100}]
{1, 1, 1, 2, 3, 4, 5, 7, 8, 11, 12, 16, 18, 23, 24, 31, 33, 41, 43, 53, 55, 67, 69, 83, 86, 102, 104,

周长为n, 有a(n)个5边为整数的5边形。
Table[Length@Select[IntegerPartitions[n, {5}], Max[#]2<n &], {n, 5, 100}]
{1, 1, 2, 2, 4, 5, 8, 9, 14, 16, 23, 25, 35, 39, 52, 57, 74, 81, 103, 111, 139, 150, 184, 197, 239,

周长为n, 有a(n)个6边为整数的6边形。
Table[Length@Select[IntegerPartitions[n, {6}], Max[#]2<n &], {n, 6, 100}]
{1, 1, 2, 3, 4, 6, 9, 12, 16, 22, 28, 37, 46,  59, 71,  91, 107, 134, 157, 193, 222, 271, 308, 371,

周长为n, 有a(n)个7边为整数的7边形。
Table[Length@Select[IntegerPartitions[n, {7}], Max[#]2<n &], {n, 7, 100}]
{1, 1, 2, 3, 5, 6, 10, 13, 19, 24, 34, 42, 58, 70, 93, 112, 145, 171, 218, 256, 320, 372, 458, 528,

周长为n, 有a(n)个8边为整数的8边形。
Table[Length@Select[IntegerPartitions[n, {8}], Max[#]2<n &], {n, 8, 100}]
{1, 1, 2, 3, 5, 7, 10, 14, 20, 27, 36, 48, 63, 82, 104, 134, 167, 211, 258, 322, 389, 480, 572, 698,   

周长为n, 有a(n)个9边为整数的9边形。
Table[Length@Select[IntegerPartitions[n, {9}], Max[#]2<n &], {n, 9, 100}]
{1, 1, 2, 3, 5, 7, 11, 14, 21, 28, 39, 50, 69, 87, 116, 145, 189, 233, 299, 363, 458, 553, 687, 820,