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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
OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(5) + sqrt(6))^4 = 241 + 44*sqrt(30). - Ant King, Dec 30 2011
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