Sequences
392,541 sequences
- Theta series of direct sum of 3 copies of E_8 lattice (the Niemeier lattice of type E_8^3).A008411
Theta series of direct sum of 3 copies of E_8 lattice (the Niemeier lattice of type E_8^3).
- Coordination sequence for 4-dimensional cubic lattice (points on surface of 4-dimensional cross-polytope).A008412
Coordination sequence for 4-dimensional cubic lattice (points on surface of 4-dimensional cross-polytope).
- Coordination sequence for 5-dimensional cubic lattice.A008413
Coordination sequence for 5-dimensional cubic lattice.
- Coordination sequence for 6-dimensional cubic lattice.A008414
Coordination sequence for 6-dimensional cubic lattice.
- Coordination sequence for 7-dimensional cubic lattice.A008415
Coordination sequence for 7-dimensional cubic lattice.
- Coordination sequence for 8-dimensional cubic lattice.A008416
Coordination sequence for 8-dimensional cubic lattice.
- Crystal ball sequence for 8-dimensional cubic lattice.A008417
Crystal ball sequence for 8-dimensional cubic lattice.
- Coordination sequence for 9-dimensional cubic lattice.A008418
Coordination sequence for 9-dimensional cubic lattice.
- Crystal ball sequence for 9-dimensional cubic lattice.A008419
Crystal ball sequence for 9-dimensional cubic lattice.
- Coordination sequence for 10-dimensional cubic lattice.A008420
Coordination sequence for 10-dimensional cubic lattice.
- Crystal ball sequence for 10-dimensional cubic lattice.A008421
Crystal ball sequence for 10-dimensional cubic lattice.
- Theta series of D*_5 lattice.A008422
Theta series of D*_5 lattice.
- Theta series of {D_7}* lattice.A008423
Theta series of {D_7}* lattice.
- Theta series of {D_9}* lattice.A008424
Theta series of {D_9}* lattice.
- Theta series of {D_6}* lattice.A008425
Theta series of {D_6}* lattice.
- Theta series of {D_10}* lattice.A008426
Theta series of {D_10}* lattice.
- Theta series of {D_8}* lattice.A008427
Theta series of {D_8}* lattice.
- Theta series of D_6 lattice.A008428
Theta series of D_6 lattice.
- Theta series of D_7 lattice.A008429
Theta series of D_7 lattice.
- Theta series of D_8 lattice.A008430
Theta series of D_8 lattice.
- Theta series of D_9 lattice.A008431
Theta series of D_9 lattice.
- Theta series of D_10 lattice.A008432
Theta series of D_10 lattice.
- Theta series of {D_5}^{+} packing.A008433
Theta series of {D_5}^{+} packing.
- Theta series of {D_6}^{+} lattice.A008434
Theta series of {D_6}^{+} lattice.
- Theta series of {D_7}^{+} packing.A008435
Theta series of {D_7}^{+} packing.
- Theta series of {D_9}^{+} packing.A008436
Theta series of {D_9}^{+} packing.
- Expansion of Jacobi theta constant theta_2^3 /8.A008437
Expansion of Jacobi theta constant theta_2^3 /8.
- Sum of divisors of 2*n + 1.A008438
Sum of divisors of 2*n + 1.
- Expansion of Jacobi theta constant theta_2^5 /32.A008439
Expansion of Jacobi theta constant theta_2^5 /32.
- Expansion of Jacobi theta constant theta_2^6 /(64q^(3/2)).A008440
Expansion of Jacobi theta constant theta_2^6 /(64q^(3/2)).
- Number of ordered ways of writing n as the sum of 2 triangular numbers.A008441
Number of ordered ways of writing n as the sum of 2 triangular numbers.
- Expansion of Jacobi theta constant (theta_2(2z))^2/4.A008442
Expansion of Jacobi theta constant (theta_2(2z))^2/4.
- Number of ordered ways of writing n as the sum of 3 triangular numbers.A008443
Number of ordered ways of writing n as the sum of 3 triangular numbers.
- Theta series of A_4 lattice.A008444
Theta series of A_4 lattice.
- Theta series of A_5 lattice.A008445
Theta series of A_5 lattice.
- Theta series of A_6 lattice.A008446
Theta series of A_6 lattice.
- Theta series of A_7 lattice.A008447
Theta series of A_7 lattice.
- Theta series of A_8 lattice.A008448
Theta series of A_8 lattice.
- Theta series of A_9 lattice.A008449
Theta series of A_9 lattice.
- Theta series of A_10 lattice.A008450
Theta series of A_10 lattice.
- Number of ways of writing n as a sum of 7 squares.A008451
Number of ways of writing n as a sum of 7 squares.
- Number of ways of writing n as a sum of 9 squares.A008452
Number of ways of writing n as a sum of 9 squares.
- Number of ways of writing n as a sum of 11 squares.A008453
Number of ways of writing n as a sum of 11 squares.
- Tenth powers: a(n) = n^10.A008454
Tenth powers: a(n) = n^10.
- 11th powers: a(n) = n^11.A008455
11th powers: a(n) = n^11.
- 12th powers: a(n) = n^12.A008456
12th powers: a(n) = n^12.
- a(n) = Sum_{ d >= 1, d divides n} (-1)^(n-d)*d^3.A008457
a(n) = Sum_{ d >= 1, d divides n} (-1)^(n-d)*d^3.
- Coordination sequence for hexagonal lattice.A008458
Coordination sequence for hexagonal lattice.
- Square the entries of Pascal's triangle.A008459
Square the entries of Pascal's triangle.
- Take sum of squares of digits of previous term; start with 6.A008460
Take sum of squares of digits of previous term; start with 6.