Constants For Normal Squares
If the squares are normal, the constant for the power-squares can be determined as follows:
Bimagic series totals for bimagic squares are also linked to the square-pyramidal number sequence is as follows :-
Squares 0, 1, 4, 9, 16, 25, 36, 49, .... (sequence A000290 in OEIS)
Sum of Squares 0, 1, 5, 14, 30, 55, 91, 140, 204, 285, ... (sequence A000330 in OEIS) )number of units in a square-based pyramid)
The bimagic series is the 1st, 4th, 9th in this series (divided by 1, 2, 3, n) etc. so values for the rows and columns in order-1, order-2, order-3 Bimagic squares would be 1, 15, 95, 374, 1105, 2701, 5775, 11180, ... (sequence A052459 in OEIS)
The trimagic series would be related in the same way to the hyper-pyramidal sequence of nested cubes.
Cubes 0, 1, 8, 27, 64, 125, 216, ... (sequence A000578 in OEIS)
Sum of Cubes 0, 1, 9, 36, 100, ... (sequence A000537 in OEIS)
Value for Trimagic squares 1, 50, 675, 4624, ... (sequence A052460 in OEIS)
Similarly the tetramagic sequence
4-Power 0, 1, 16, 81, 256, 625, 1296, ... (sequence A000583 in OEIS)
Sum of 4-Power 0, 1, 17, 98, 354, 979, 2275, ... (sequence A000538 in OEIS)
Sums for Tetramagic squares 0, 1, 177, ... (sequence A052461 in OEIS)
Read more about this topic: Multimagic Square
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