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A087125 Indices n of hex numbers H(n) that are also triangular. 2
0, 5, 54, 539, 5340, 52865, 523314, 5180279, 51279480, 507614525, 5024865774, 49741043219, 492385566420, 4874114620985, 48248760643434, 477613491813359, 4727886157490160, 46801248083088245, 463284594673392294, 4586044698650834699, 45397162391834954700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Eric Weisstein's World of Mathematics, Hex Number

Index entries for linear recurrences with constant coefficients, signature (11,-11,1).

FORMULA

G.f.: (-x^2+5*x)/((1-x)*(1-10*x+x^2)).

a(n) = 11*a(n-1)-11*a(n-2)+a(n-3) for n>2. - Colin Barker, Jun 23 2015

a(n) = (-4-(5-2*sqrt(6))^n*(-2+sqrt(6))+(2+sqrt(6))*(5+2*sqrt(6))^n)/8. - Colin Barker, Mar 05 2016

MATHEMATICA

CoefficientList[Series[(-x^2+5*x)/((1-x)*(1-10*x+x^2)), {x, 0, 25}], x] (* G. C. Greubel, Nov 04 2017 *)

PROG

(PARI) concat(0, Vec(x*(x-5)/((x-1)*(x^2-10*x+1)) + O(x^50))) \\ Colin Barker, Jun 23 2015

(MAGMA) [Round((-4-(5-2*Sqrt(6))^n*(-2+Sqrt(6)) + (2+Sqrt(6))*(5 + 2*Sqrt(6))^n)/8): n in [0..25]]; // G. C. Greubel, Nov 04 2017

CROSSREFS

Cf. A006244, A031138.

Sequence in context: A221544 A268882 A229298 * A110430 A110432 A215542

Adjacent sequences:  A087122 A087123 A087124 * A087126 A087127 A087128

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Aug 14 2003

STATUS

approved

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Last modified January 29 04:22 EST 2022. Contains 350672 sequences. (Running on oeis4.)