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A247375 Numbers n such that floor(n/2) is a square. 8
0, 1, 2, 3, 8, 9, 18, 19, 32, 33, 50, 51, 72, 73, 98, 99, 128, 129, 162, 163, 200, 201, 242, 243, 288, 289, 338, 339, 392, 393, 450, 451, 512, 513, 578, 579, 648, 649, 722, 723, 800, 801, 882, 883, 968, 969, 1058, 1059, 1152, 1153, 1250, 1251, 1352, 1353 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Union of A001105 and A058331.

Squares of the sequence are listed in A055792.

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

FORMULA

G.f.: x*( 1 + x - x^2 + 3*x^3 ) / ( (1 - x)^3*(1 + x)^2 ).

a(n) = 1 + ( 2*n*(n-1) + (2*n-3)*(-1)^n - 1 )/4.

a(n+1) = 1 + A213037(n).

MATHEMATICA

Select[Range[0, 1400], IntegerQ[Sqrt[Floor[#/2]]] &]

PROG

(MAGMA) [n: n in [0..1400] | IsSquare(Floor(n div 2))];

(Sage) [n for n in [0..1400] if is_square(floor(n/2))]

CROSSREFS

Cf. A001105, A055792, A058331, A213037.

Cf. A130404: numbers n such that floor(n/2) is a triangular number.

Sequence in context: A260020 A104577 A309017 * A282508 A103026 A098506

Adjacent sequences:  A247372 A247373 A247374 * A247376 A247377 A247378

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Sep 15 2014

STATUS

approved

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Last modified January 28 22:35 EST 2020. Contains 331328 sequences. (Running on oeis4.)