cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A069920 Number of noninvertible n X n matrices mod 6 (i.e., over the ring Z_6).

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%I A069920 #11 Jul 12 2025 08:34:46
%S A069920 4,1008,8190720,2332005728256,23674927650073214976,
%T A069920 8618480376852061696039059456,112746432609478969278312620164116381696,
%U A069920 53053593891934168169788522401776516627950360068096,898369021875992553077210146021642426986208034219512412195782656
%N A069920 Number of noninvertible n X n matrices mod 6 (i.e., over the ring Z_6).
%F A069920 a(n) = 6^(n^2) - A065498(n).
%F A069920 a(n) ~ c * 6^(n^2), where c = 1 - A048651 * A100220 = 0.838242256946... . - _Amiram Eldar_, Jul 12 2025
%t A069920 a[n_] := 6^(n^2) * (1 - Product[(1 - 1/2^k) * (1 - 1/3^k), {k, 1, n}]); Array[a, 10] (* _Amiram Eldar_, Jul 12 2025 *)
%o A069920 (PARI) a(n) = 6^(n^2)*(1-prod(k=1,n,(1-1/2^k)*(1-1/3^k)));
%Y A069920 Cf. A048651, A065498, A069580, A100220 .
%K A069920 nonn
%O A069920 1,1
%A A069920 Sharon Sela (sharonsela(AT)hotmail.com), May 05 2002
%E A069920 More terms from _Benoit Cloitre_, May 11 2002