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A039835 Indices of triangular numbers which are also heptagonal. 3
1, 10, 493, 3382, 158905, 1089154, 51167077, 350704366, 16475640049, 112925716858, 5305104928861, 36361730124070, 1708227311453353, 11708364174233842, 550043889183050965, 3770056902373173214, 177112424089630957537, 1213946614199987541226 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

From Ant King, Oct 19 2011: (Start)

lim(n->Infinity,a(2n+1)/a(2n))=1/2(47+21*sqrt(5)).

lim(n->Infinity,a(2n)/a(2n-1))=1/2(7+3*sqrt(5)).

(End)

LINKS

Colin Barker, Table of n, a(n) for n = 1..798

Eric Weisstein's World of Mathematics, Heptagonal Triangular Number

Index entries for linear recurrences with constant coefficients, signature (1,322,-322,-1,1).

FORMULA

G.f.: (-2x^4-9x^3+161x^2+9x+1)/[(1-x)(1-18x+x^2)(1+18x+x^2)].

a(n+2) = 322*a(n+1)-a(n)+160 a(n+1) = 161*a(n)+80+36*(20*a(n)^2+20*a(n)+9)^0.5 - Richard Choulet, Sep 29 2007

From Ant King, Oct 19 2011: (Start)

a(n) = a(n-1)+322a(n-2)-322a(n-3)-a(n-4)+a(n-5).

a(n) = 1/20*sqrt(5)*(( sqrt(5)-(-1)^n)*(2+ sqrt(5))^(2n-1)+( sqrt(5)+(-1)^n)*(2- sqrt(5))^(2n-1)-2* sqrt(5)).

a(n) = floor(1/20* sqrt(5)*(sqrt(5)-(-1)^n)*(2+ sqrt(5))^(2n-1))(End)

MATHEMATICA

LinearRecurrence[{1, 322, -322, -1, 1}, {1, 10, 493, 3382, 158905}, 16] (* Ant King, Oct 19 2011 *)

PROG

(PARI) Vec((-2*x^4-9*x^3+161*x^2+9*x+1)/((1-x)*(1-18*x+x^2)*(1+18*x+x^2))+O(x^99))

CROSSREFS

Cf. A046193, A046194.

Sequence in context: A200458 A223122 A071096 * A293090 A127947 A095232

Adjacent sequences:  A039832 A039833 A039834 * A039836 A039837 A039838

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified August 23 11:47 EDT 2019. Contains 326222 sequences. (Running on oeis4.)