login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A057780 Multiples of 3 that are one less than a perfect square. 6
0, 3, 15, 24, 48, 63, 99, 120, 168, 195, 255, 288, 360, 399, 483, 528, 624, 675, 783, 840, 960, 1023, 1155, 1224, 1368, 1443, 1599, 1680, 1848, 1935, 2115, 2208, 2400, 2499, 2703, 2808, 3024, 3135, 3363, 3480, 3720, 3843, 4095, 4224, 4488, 4623, 4899, 5040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also, numbers of the form 9*m^2+6*m, m an integer. - Jason Kimberley, Nov 08 2012

k is in this list iff k+1 is in the support of A033684. - Jason Kimberley, Nov 13 2012

LINKS

Jason Kimberley, Table of n, a(n) for n = 1..2001

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

FORMULA

a(n) = A001651(n)^2 - 1 = 3 * A001082(n).

G.f.: 3*x^2*(1+4*x+x^2) / ((1-x)^3*(1+x)^2). - Colin Barker, Nov 24 2012

From Colin Barker, Dec 26 2015: (Start)

a(n) = 3/8*(6*n^2-2*((-1)^n+3)*n+(-1)^n-1).

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>5.

(End)

MATHEMATICA

Select[3*Range[0, 2000], IntegerQ[Sqrt[#+1]]&] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {0, 3, 15, 24, 48}, 50] (* Harvey P. Dale, Sep 10 2019 *)

PROG

(MAGMA) a:=func<n|9*n^2+6*n>; [0]cat[a(n*m):m in[-1, 1], n in[1..24]]; // Jason Kimberley, Nov 09 2012

(PARI) concat(0, Vec(3*x^2*(1+4*x+x^2)/((1-x)^3*(1+x)^2) + O(x^100))) \\ Colin Barker, Dec 26 2015

CROSSREFS

Numbers of the form 9n^2+kn, for integer n: A016766 (k=0), A132355 (k=2), A185039 (k=4), this sequence (k=6), A218864 (k=8). - Jason Kimberley, Nov 08 2012

Sequence in context: A161467 A101133 A061386 * A274697 A129024 A018982

Adjacent sequences:  A057777 A057778 A057779 * A057781 A057782 A057783

KEYWORD

nonn,easy

AUTHOR

Benjamin Geiger (benjamin_geiger(AT)yahoo.com), Nov 02 2000

EXTENSIONS

Since this is a list, offset corrected to 1 by Jason Kimberley, Nov 09 2012

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 25 17:14 EDT 2021. Contains 347659 sequences. (Running on oeis4.)