	Multi-dimensional Crystallography and Number Theory
$E_{d}$	E₁	E₂	E₃	E₄	E₅	E₆	E₇	E₈	E₉	E₁₀	E₁₁	E₁₂	E₁₃
$N_{d}$	2	6	10	24	38	78	118	224	330	584	838	1420	2002
$K_{d}$ (positive)	1	5	5	19	19	59	59	165	165	419	419	1001	1001
$N_{d} + K_{d}$	3	11	15	43	57	137	177	389	495	1003	1257	2421	3003
$σ_{{(d / 2)}^{2}} + σ_{{(d / 2)}^{2} - 1}$	-	1	-	17	-	137	-	611	-	1839	-	4405	-
$T_{d} = \sum_{d - 1}^{d + 1} K_{d}$	7	11	29	43	97	137	283	389	749	1003	1839	2421	4259
$S_{d} = Σ_{1}^{d} (N_{d} / 2)$	1	4	9	21	40	79	138	250	415	707	1126	1836	2837
$q_{d} = (\begin{matrix} 3 + d \\ 4 \end{matrix})$	1	5	15	35	70	126	210	330	495	715	1001	1365	1820