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A050271 Numbers n such that n = floor(sqrt(n)*ceiling(sqrt(n))). 1
1, 2, 3, 4, 7, 8, 9, 14, 15, 16, 23, 24, 25, 34, 35, 36, 47, 48, 49, 62, 63, 64, 79, 80, 81, 98, 99, 100, 119, 120, 121, 142, 143, 144, 167, 168, 169, 194, 195, 196, 223, 224, 225, 254, 255, 256, 287, 288, 289, 322, 323, 324, 359, 360, 361, 398, 399, 400 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Is a(n) asymptotic to C*n^(3/2) where 1/2 < C < 1?

Consists exactly of numbers of the forms k^2 - 2, k^2 - 1, and k^2. As such, is asymptotic to 1/9 * n^2. - Ivan Neretin, Feb 08 2017

LINKS

Ivan Neretin, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,2,-2,0,-1,1).

FORMULA

a(n) = floor((n + 4)/3)^2 + ((n + 1) mod 3) - 2. - Ivan Neretin, Feb 08 2017

From Colin Barker, Feb 09 2017: (Start)

a(n) = a(n-1) + 2*a(n-3) - 2*a(n-4) - a(n-6) + a(n-7) for n>7.

G.f.: x*(1 + x + x^2 - x^3 + x^4 - x^5) / ((1 - x)^3*(1 + x + x^2)^2).

(End)

MATHEMATICA

Select[Range@400, Floor[(r = Sqrt@#)*Ceiling@r] == # &] (* Ivan Neretin, Feb 08 2017 *)

PROG

(PARI) isok(n) = floor(sqrt(n)*ceil(sqrt(n))) == n; \\ Michel Marcus, Nov 22 2013

(PARI) Vec(x*(1 + x + x^2 - x^3 + x^4 - x^5) / ((1 - x)^3*(1 + x + x^2)^2) + O(x^100)) \\ Colin Barker, Feb 09 2017

CROSSREFS

Cf. A000290, A005563, A008865.

Sequence in context: A023774 A319837 A321699 * A322742 A307561 A152037

Adjacent sequences:  A050268 A050269 A050270 * A050272 A050273 A050274

KEYWORD

nonn,easy

AUTHOR

Benoit Cloitre, May 10 2003

EXTENSIONS

Data corrected by Michel Marcus and Benoit Cloitre, Nov 22 2013

STATUS

approved

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)