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%I #22 Nov 23 2022 19:41:34
%S 0,1,2,3,6,17,34,99,198,577,1154,3363,6726,19601,39202,114243,228486,
%T 665857,1331714,3880899,7761798,22619537,45239074,131836323,263672646,
%U 768398401,1536796802,4478554083,8957108166,26102926097,52205852194,152139002499,304278004998,886731088897
%N Numbers such that floor(a(n)^2 / 8) is again a square.
%C Or: Numbers whose square, with its last base-8 digit dropped, is again a square. (Except maybe for the 3 initial terms whose square has only 1 digit in base 8.)
%C See A204504 for the squares resulting from truncation of a(n)^2, and A204512 for their square roots. - _M. F. Hasler_, Sep 28 2014
%H M. F. Hasler, <a href="/wiki/M. F. Hasler/Truncated_squares">Truncated squares</a>, OEIS wiki, Jan 16 2012
%H <a href="/index/Sq#sqtrunc">Index to sequences related to truncating digits of squares</a>.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1).
%F G.f. = (x^2 + 2*x^3 - 3*x^4 - 6*x^5)/(1 - 6*x^2 + x^4).
%F a(n) = sqrt(A055872(n)). - _M. F. Hasler_, Sep 28 2014
%F a(2n) = A001541(n-1). a(2n+1) = A003499(n-1). - _R. J. Mathar_, Feb 05 2020
%p A204514 := proc(n) coeftayl((x^2+2*x^3-3*x^4-6*x^5)/(1-6*x^2+x^4), x=0, n); end proc: seq(A204514(n), n=1..30); # _Wesley Ivan Hurt_, Sep 28 2014
%t CoefficientList[Series[(x^2 + 2*x^3 - 3*x^4 - 6*x^5)/(x (1 - 6*x^2 + x^4)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 28 2014 *)
%t LinearRecurrence[{0,6,0,-1},{0,1,2,3,6},40] (* _Harvey P. Dale_, Nov 23 2022 *)
%o (PARI) b=8;for(n=0,1e7,issquare(n^2\b) & print1(n","))
%o (PARI) A204514(n)=polcoeff((x + 2*x^2 - 3*x^3 - 6*x^4)/(1 - 6*x^2 + x^4+O(x^(n+!n))),n-1,x)
%Y Cf. A031149=sqrt(A023110) (base 10), A204502=sqrt(A204503) (base 9), A204516=sqrt(A055859) (base 7), A204518=sqrt(A055851) (base 6), A204520=sqrt(A055812) (base 5), A004275=sqrt(A055808) (base 4), A001075=sqrt(A055793) (base 3), A001541=sqrt(A055792) (base 2).
%Y Cf. A003499, A055872, A204504, A204512.
%K nonn,easy
%O 1,3
%A _M. F. Hasler_, Jan 15 2012
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