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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A276599 Values of n such that n^2 + 5 is a triangular number (A000217). 5
1, 4, 10, 25, 59, 146, 344, 851, 2005, 4960, 11686, 28909, 68111, 168494, 396980, 982055, 2313769, 5723836, 13485634, 33360961, 78600035, 194441930, 458114576, 1133290619, 2670087421, 6605301784, 15562409950, 38498520085, 90704372279, 224385818726 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

FORMULA

a(n) = 6*a(n-2)-a(n-4) for n>4.

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

EXAMPLE

4 is in the sequence because 4^2+5 = 21, which is a triangular number.

MATHEMATICA

CoefficientList[Series[(1 + x)*(1 + 3*x + x^2)/((1 + 2*x - x^2)*(1 - 2*x - x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 07 2016 *)

LinearRecurrence[{0, 6, 0, -1}, {1, 4, 10, 25}, 30] (* Harvey P. Dale, Feb 13 2017 *)

PROG

(PARI) Vec(x*(1+x)*(1+3*x+x^2)/((1+2*x-x^2)*(1-2*x-x^2)) + O(x^40))

(PARI) a(n)=([0, 1; -1, 6]^(n\2)*if(n%2, [1; 10], [-1; 4]))[1, 1] \\ Charles R Greathouse IV, Sep 07 2016

CROSSREFS

Cf. A000217, A230044.

Cf. A001109 (k=0), A106328 (k=1), A077241 (k=2), A276598 (k=3), A276600 (k=6), A276601 (k=9), A276602 (k=10), where k is the value added to n^2.

Sequence in context: A159297 A248731 A279101 * A281867 A298806 A033539

Adjacent sequences:  A276596 A276597 A276598 * A276600 A276601 A276602

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 07 2016

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 25 07:12 EDT 2019. Contains 321468 sequences. (Running on oeis4.)