Voozh

A048904

Indices of heptagonal numbers (A000566) which are also octagonal.

1, 345, 166145, 80081401, 38599068993, 18604671173081, 8967412906355905, 4322274416192372985, 2083327301191817422721, 1004159436900039805378393, 484002765258517994374962561, 233288328695168773248926575865, 112444490428306090187988234604225, 54198011098114840301837080152660441

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->oo} a(n)/a(n-1) = (sqrt(5) + sqrt(6))^4 = 241 + 44*sqrt(30). - Ant King, Dec 30 2011

REFERENCES

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 41.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number.

Index entries for linear recurrences with constant coefficients, signature (483,-483,1).

FORMULA

G.f.: x*(-1 + 138*x + 7*x^2) / ( (x-1)*(x^2 - 482*x + 1) ). - R. J. Mathar, Dec 21 2011

From Ant King, Dec 30 2011: (Start)

a(n) = 482*a(n-1) - a(n-2) - 144.

a(n) = (1/60)*((3*sqrt(5) + sqrt(6))*(sqrt(5) + sqrt(6))^(4*n-3) + (3*sqrt(5) - sqrt(6))*(sqrt(5) - sqrt(6))^(4*n-3) + 18).

a(n) = ceiling((1/60)*(3*sqrt(5) + sqrt(6))*(sqrt(5) + sqrt(6))^(4*n-3)). (End)