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URL: https://oeis.org/A048904

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A048904
Indices of heptagonal numbers (A000566) which are also octagonal.
3
1, 345, 166145, 80081401, 38599068993, 18604671173081, 8967412906355905, 4322274416192372985, 2083327301191817422721, 1004159436900039805378393, 484002765258517994374962561, 233288328695168773248926575865, 112444490428306090187988234604225, 54198011098114840301837080152660441
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
Eric Weisstein's World of Mathematics, Octagonal Heptagonal Number.
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)
MATHEMATICA
LinearRecurrence[{483, -483, 1}, {1, 345, 166145}, 30]
PROG
(Magma) I:=[1, 345, 166145]; [n le 3 select I[n] else 483*Self(n-1)-483*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011
CROSSREFS
Sequence in context: A333079 A236731 A138043 * A139266 A063536 A045102
KEYWORD
nonn,easy
STATUS
approved