A204518 Numbers such that floor(a(n)^2 / 6) is a square.

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

Offset

1,3

Comments

Or: Numbers whose 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 entries for linear recurrences with constant coefficients, signature (0,0,10,0,0,-1).

Formula

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

From Colin Barker, Sep 18 2014: (Start)

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). (End)

a(3n+2) = A001079(n). a(3n) = A087799(n-1). - R. J. Mathar, Feb 05 2020

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: A007695 A296261 A133662 * A336991 A223545 A088938

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