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A276602 Values of n such that n^2 + 10 is a triangular number (A000217). 5
0, 9, 54, 315, 1836, 10701, 62370, 363519, 2118744, 12348945, 71974926, 419500611, 2445028740, 14250671829, 83059002234, 484103341575, 2821561047216, 16445262941721, 95850016603110, 558654836676939, 3256079003458524, 18977819184074205, 110610836100986706 (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) = -(9*((3-2*sqrt(2))^n*(3+2*sqrt(2))+(-3+2*sqrt(2))*(3+2*sqrt(2))^n)) / (4*sqrt(2)).

a(n) = 9*A001109(n-1).

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

G.f.: 9*x^2 / (1-6*x+x^2).

EXAMPLE

9 is in the sequence because 9^2+10 = 91, which is a triangular number.

MATHEMATICA

CoefficientList[Series[9*x/(1 - 6*x + x^2), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 07 2016 *)

PROG

(PARI) concat(0, Vec(9*x^2/(1-6*x+x^2) + O(x^30)))

CROSSREFS

Cf. A000217, A230044.

Cf. A001109 (k=0), A106328 (k=1), A077241 (k=2), A276598 (k=3), A276599 (k=5), A276600 (k=6), A276601 (k=9), where k is the value added to n^2.

Sequence in context: A001392 A188428 A243415 * A079764 A079761 A115784

Adjacent sequences:  A276599 A276600 A276601 * A276603 A276604 A276605

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 07 2016

STATUS

approved

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Last modified October 20 23:39 EDT 2018. Contains 316405 sequences. (Running on oeis4.)