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A276598 Values of n such that n^2 + 3 is a triangular number (A000217). 5
0, 5, 30, 175, 1020, 5945, 34650, 201955, 1177080, 6860525, 39986070, 233055895, 1358349300, 7917039905, 46143890130, 268946300875, 1567533915120, 9136257189845, 53250009223950, 310363798153855, 1808932779699180, 10543232880041225, 61450464500548170 (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 (6,-1).

FORMULA

a(n) = 5*A001109(n-1).

a(n) = -(5*((3-2*sqrt(2))^n*(3+2*sqrt(2))+(-3+2*sqrt(2))*(3+2*sqrt(2))^n)) / (4*sqrt(2)).

a(n) = 6*a(n-1)-a(n-2) for n>2.

G.f.: 5*x^2 / (1-6*x+x^2).

EXAMPLE

5 is in the sequence because 5^2+3 = 28, which is a triangular number.

MATHEMATICA

CoefficientList[Series[5*x/(1 - 6*x + x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 07 2016 *)

PROG

(PARI) concat(0, Vec(5*x^2/(1-6*x+x^2) + O(x^30)))

(PARI) a(n)=([0, 1; -1, 6]^n*[-5; 0])[1, 1] \\ Charles R Greathouse IV, Sep 07 2016

CROSSREFS

Cf. A000217, A230044.

Cf. A001109 (k=0), A106328 (k=1), A077241 (k=2), A276599 (k=5), A276600 (k=6), A276601 (k=9), A276602 (k=10), where k is the value added to n^2.

Sequence in context: A111469 A241588 A229246 * A057088 A156195 A105481

Adjacent sequences:  A276595 A276596 A276597 * A276599 A276600 A276601

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 07 2016

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)