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A264081 The sum of the 2 X 2 idempotent matrices over Z/nZ is congruent to {{a(n),0}, {0,a(n)}} (mod n). 0
0, 0, 1, 1, 1, 2, 1, 1, 1, 8, 1, 2, 1, 8, 14, 1, 1, 8, 1, 16, 7, 8, 1, 14, 1, 8, 1, 26, 1, 22, 1, 1, 14, 8, 18, 26, 1, 8, 1, 8, 1, 14, 1, 26, 5, 8, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

The 2 X 2 idempotent matrices over Z/3Z are {{0, 0}, {0, 0}}, {{0, 0}, {0,1}}, {{0, 0}, {1, 1}}, {{0, 0}, {2, 1}}, {{0, 1}, {0, 1}}, {{0, 2}, {0, 1}}, {{1, 0}, {0, 0}}, {{1, 0}, {0, 1}}, {{1, 0}, {1, 0}}, {{1, 0}, {2, 0}}, {{1, 1}, {0, 0}}, {{1, 2}, {0, 0}}, {{2, 1}, {1, 2}}, {{2, 2}, {2, 2}}. Their sum is {{10, 9}, {9, 10}} == 1*{{1, 0}, {0, 1}} (mod 3) and therefore a(3) = 1.

MATHEMATICA

K[n_] := K[n] = Mod[Sum[If[ Mod[{{a, b}, {c, d}}.{{a, b}, {c, d}} - {{a, b}, {c, d}}, n] == 0{{a, b}, {c, d}}, {{a, b}, {c, d}}, 0], {a, n}, {b, n}, {c, n}, {d, n}], n]; Table[K[n][[1, 1]], {n, 1, 22}]

PROG

(PARI) a(n) = lift(sum(i=0, n-1, sum(j=0, n-1, sum(k=0, n-1, sum(l=0, n-1, m = Mod([i, j; k, l], n); if ((m^2 == m), m[1, 1])))))); \\ Michel Marcus, Apr 04 2016

CROSSREFS

Cf. A226756.

Sequence in context: A171660 A157117 A322143 * A061538 A123602 A208896

Adjacent sequences:  A264078 A264079 A264080 * A264082 A264083 A264084

KEYWORD

nonn,more

AUTHOR

José María Grau Ribas, Nov 03 2015

STATUS

approved

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)