how to make integer pyramid from 20201994 number.
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how to make integer pyramid from 20201994 number.
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In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square base. Square pyramidal numbers also solve the problem of counting the number of squares in an n × n grid.
The first few square pyramidal numbers are:
1, 5, 14, 30, 55, 91, 140, 204, 285, 385, 506, 650, 819, ... (sequence A000330 in the OEIS).
These numbers can be expressed in a formula as
This is a special case of Faulhaber's formula, and may be proved by a mathematical induction.[1] An equivalent formula is given in Fibonacci's Liber Abaci (1202, ch. II.12).
In modern mathematics, figurate numbers are formalized by the Ehrhart polynomials. The Ehrhart polynomial L(P,t) of a polyhedron P is a polynomial that counts the number of integer points in a copy of P that is expanded by multiplying all its coordinates by the number t. The Ehrhart polynomial of a pyramid whose base is a unit square with integer coordinates, and whose apex is an integer point at height one above the base plane, is
(t + 1)(t + 2)(2t + 3)
/
6
= Pt + 1.[2]