First of all sorry if i am mistaking word translation, i am not a native English speaker.
I got a problem which i partially solved. I must do calculations with a six-story card castle (two-dimensional pyramid of cards making triangles), and to simplify i think i already solved the general term, i got four possibilities, which i think all right:
Pn = to n, index=1 -> Σ(3n)-n
Pn = to n, index=1 -> Σ(2n) + to n-1, index=1 -> Σ(1)
Pn = (n*(n+1)/2)*3-n and
Pn = 1.5n² + 0.5n
Are them all right to calculate the cards used knowing the height of this?
Now i need to know with one of the formulas to know where will it cross a multiple of 52. In another words, i need to know when will the division of them by 52 result in an integer.
I need a justification, not a solution. How am i supposed to reach the solution?