A064276 -id:A064276 - cp's OEIS frontend

A064368 Number of 2 X 2 symmetric singular matrices with entries from {0,...,n}.

1, 4, 7, 10, 15, 18, 21, 24, 29, 36, 39, 42, 47, 50, 53, 56, 65, 68, 75, 78, 83, 86, 89, 92, 97, 108, 111, 118, 123, 126, 129, 132, 141, 144, 147, 150, 163, 166, 169, 172, 177, 180, 183, 186, 191, 198, 201, 204, 213, 228, 239, 242, 247, 250, 257, 260, 265, 268

Offset: 0

Vladeta Jovovic, Sep 27 2001

nonn

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Cf. A000010, A000188, A064276, A059306, A062801, A059976, A039623.

Cf. A001620, A306016.

f[p_, e_] := p^Floor[e/2]; a[0] = 0; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; With[{max = 100}, 1 + Range[0, max] + 2 * Accumulate[Array[a, max + 1, 0]]] (* Amiram Eldar, Nov 07 2024 *)

a(n) = n + 1 + 2*sum(k=1, n, sumdiv(k, d, issquare(d)*eulerphi(sqrtint(d)))) \\ Michel Marcus, Jun 17 2013

a(n) = n + 1 + 2*Sum_{k=1..n} Sum_{d^2|k} phi(d), where phi = Euler totient function A000010.

a(n) ~ (n/zeta(2)) * (log(n) + 3*gamma - 1 + zeta(2) - 2*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620). - Amiram Eldar, Nov 07 2024

A064363 Number of 2 X 2 regular integer matrices with elements from {0,...,n} up to row and column permutation.

Original entry on oeis.org

0, 2, 14, 51, 133, 289, 547, 954, 1546, 2380, 3508, 5005, 6915, 9347, 12353, 16028, 20468, 25790, 32054, 39427, 47965, 57833, 69155, 82082, 96682, 113192, 131720, 152429, 175467, 201075, 229305, 260492, 294700, 332182, 373138, 417751, 466201

Offset: 0

Vladeta Jovovic, Sep 25 2001

			There are 2 binary regular matrices up to row and column permutation:
[1 0] [1 1]
[0 1] [1 0].

Cf. A064276, A059306, A062801, A059976, A039623.

A059306[0] = 1; A059306[n_] := Table[{w, x, y, z} /. {ToRules[ Reduce[0 <= x <= n && 0 <= y <= n && 0 <= z <= n && w*z - x*y == 0, {x, y, z}, Integers]]}, {w, 0, n}] // Flatten[#, 1] & // Length; a[n_] := ((n + 1)*(n^3 + 3*n^2 + 4*n + 1) - A059306[n])/4; Table[Print[an = a[n]]; an, {n, 0, 36}] (* Jean-François Alcover, Nov 26 2013 *)

a(n) = ((n+1)*(n^3+3*n^2+4*n+1)-A059306(n))/4.

cp's OEIS Frontend

A064368 Number of 2 X 2 symmetric singular matrices with entries from {0,...,n}.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula