login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A154153 Indices n such that 28 plus the n-th triangular number is a perfect square. 2
6, 8, 47, 57, 278, 336, 1623, 1961, 9462, 11432, 55151, 66633, 321446, 388368, 1873527, 2263577, 10919718, 13193096, 63644783, 76895001, 370948982, 448176912, 2162049111, 2612166473, 12601345686, 15224821928, 73446025007, 88736765097, 428074804358, 517195768656 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..30.

F. T. Adams-Watters, SeqFan Discussion, Oct 2009

FORMULA

{k: 28+k*(k+1)/2 in A000290}.

Conjectures: (Start)

a(n) = +a(n-1) +6*a(n-2) -6*a(n-3) -a(n-4) +a(n-5).

G.f.: x*(-6-2*x-3*x^2+2*x^3+7*x^4)/((x-1) * (x^2-2*x-1) * (x^2+2*x-1)).

G.f.: ( 14 + 1/(x-1) + (14+29*x)/(x^2-2*x-1) + (-1-12*x)/(x^2+2*x-1) )/2. (End)

EXAMPLE

6*(6+1)/2+28 = 7^2. 8*(8+1)/2+28 = 8^2. 47*(47+1)/2+28 = 34^2. 57*(57+1)/2+28 = 41^2.

MATHEMATICA

Join[{6, 8}, Select[Range[0, 10^5], ( Ceiling[Sqrt[#*(# + 1)/2]] )^2 - #*(# + 1)/2 == 28 &]] (* G. C. Greubel, Sep 03 2016 *)

PROG

(PARI) {for (n=0, 10^9, if ( issquare(n*(n+1)\2 + 28), print1(n, ", ") ) ); }

CROSSREFS

Cf. A000217, A000290, A006451.

Sequence in context: A054102 A261063 A000380 * A164640 A223852 A227167

Adjacent sequences:  A154150 A154151 A154152 * A154154 A154155 A154156

KEYWORD

nonn,changed

AUTHOR

R. J. Mathar, Oct 18 2009

EXTENSIONS

a(21)-a(30) from Amiram Eldar, Mar 18 2019

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 March 24 01:20 EDT 2019. Contains 321444 sequences. (Running on oeis4.)