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A204518 Numbers such that floor(a(n)^2 / 6) is a square. 19
0, 1, 2, 3, 5, 10, 27, 49, 98, 267, 485, 970, 2643, 4801, 9602, 26163, 47525, 95050, 258987, 470449, 940898, 2563707, 4656965, 9313930, 25378083, 46099201, 92198402, 251217123, 456335045, 912670090, 2486793147, 4517251249, 9034502498, 24616714347 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Or: Numbers such that their square, with its last base-6 digit dropped, is again a square. (For the three initial terms whose square has only one digit in base 6, this is then meant to yield zero.)

LINKS

Table of n, a(n) for n=1..34.

Index to sequences with linear recurrences with constant coefficients, signature (0,0,10,0,0,-1).

FORMULA

a(n) = sqrt(A055851(n)).

a(n) = 10*a(n-3)-a(n-6) for n>7; G.f.: -x^2*(x+1)*(3*x^4+7*x^3-2*x^2-x-1) / (x^6-10*x^3+1). - Colin Barker, Sep 18 2014

PROG

(PARI) b=6; for(n=0, 2e9, issquare(n^2\b) & print1(n", "))

(PARI) concat(0, Vec(-x^2*(x+1)*(3*x^4+7*x^3-2*x^2-x-1)/(x^6-10*x^3+1) + O(x^100))) \\ Colin Barker, Sep 18 2014

CROSSREFS

Cf. A023110 (base 10), A204502 (base 9), A204514 (base 8), A204516 (base 7), A204520 (base 5), A004275 (base 4), A055793 (base 3), A055792 (base 2).

Sequence in context: A011833 A007695 A133662 * A223545 A088938 A000617

Adjacent sequences:  A204515 A204516 A204517 * A204519 A204520 A204521

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Jan 15 2012

EXTENSIONS

More terms from Colin Barker, Sep 18 2014

STATUS

approved

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Last modified March 31 20:49 EDT 2015. Contains 256084 sequences.