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A144065 Values of n such that the expression sqrt(4!*(n+1) + 1) yields an integer. 5
0, 1, 4, 6, 11, 14, 21, 25, 34, 39, 50, 56, 69, 76, 91, 99, 116, 125, 144, 154, 175, 186, 209, 221, 246, 259, 286, 300, 329, 344, 375, 391, 424, 441, 476, 494, 531, 550, 589, 609, 650, 671, 714, 736, 781, 804, 851, 875, 924, 949, 1000, 1026, 1079, 1106, 1161, 1189, 1246, 1275, 1334, 1364, 1425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Integers of form m*(m+5)/6 (nonnegative values of m are listed in A032766). - Bruno Berselli, Jul 18 2016

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6). - Jaume Oliver Lafont, Jan 21 2009

a(n) = (-3 + 2*(-1)^n*n + 3*(-1)^n + 6*n^2 + 18*n)/16. - Alexander R. Povolotsky, Jan 27 2009

a(n) = A001318(n+1) - 1. - Peter Bala, Mar 22 2009

G.f.: x*(1 + 3*x - x^3)/((1 + x)^2*(1 - x)^3). - Jaume Oliver Lafont, Aug 31 2009

a(n) = Sum_{i=1..n+3} numerator(i/2) - denominator(i/2). - Wesley Ivan Hurt, Feb 26 2017

MAPLE

seq(seq(((24*a+b)^2-25)/24, b=[5, 7, 11, 13, 17, 19, 23, 25]), a=0..10); # Robert Israel, Jul 15 2016

MATHEMATICA

LinearRecurrence[{0, 3, 0, -3, 0, 1}, {0, 1, 4, 6, 11, 14}, 50] (* G. C. Greubel, Jul 15 2016 *)

Select[Range[0, 1500], IntegerQ[Sqrt[4!(#+1)+1]]&] (* Harvey P. Dale, Sep 20 2019 *)

PROG

(PARI) j=[]; for(n=0, 300, if((floor(sqrt(4!*(n+1) + 1))) == ceil(sqrt(4!*(n+1) + 1)), j=concat(j, n))); j

(MAGMA) [(-3+2*(-1)^n*n+3*(-1)^n+6*n^2+18*n)/16: n in [0..60]]; // Vincenzo Librandi, Jul 16 2016

CROSSREFS

Cf. A007310, A038179, A075889.

Cf. sequences of the form m*(m+k)/(k+1) listed in A274978. [Bruno Berselli, Jul 25 2016]

Sequence in context: A153357 A310591 A002732 * A036831 A084263 A232807

Adjacent sequences:  A144062 A144063 A144064 * A144066 A144067 A144068

KEYWORD

nonn,easy

AUTHOR

Alexander R. Povolotsky, Sep 09 2008

STATUS

approved

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Last modified October 23 11:19 EDT 2019. Contains 328345 sequences. (Running on oeis4.)