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A203136 Indices of decagonal numbers that are also hexagonal. 2
1, 20, 667, 22646, 769285, 26133032, 887753791, 30157495850, 1024467105097, 34801724077436, 1182234151527715, 40161159427864862, 1364297186395877581, 46345943178031972880, 1574397770866691200327, 53483178266289468838226, 1816853663282975249299345 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^4=17+12*sqrt(2).
LINKS
FORMULA
G.f.: x(1-15*x+2*x^2) / ((1-x)*(1-34*x+x^2))
a(n) = 35*a(n-1)-35*a(n-2)+a(n-3)
a(n) = 34*a(n-1)-a(n-2)-12
a(n) = 1/16 *((3-sqrt(2))*(1+sqrt(2))^(4*n-2)+(3+sqrt(2))*(1-sqrt(2))^(4*n-2)+6)
a(n) = ceiling(1/16*(3-sqrt(2))*(1+sqrt(2))^(4*n-2))
EXAMPLE
The second decagonal number which is also hexagonal is A001107(20) = 1540. Hence a(2) = 20.
MATHEMATICA
LinearRecurrence[{35, -35, 1}, {1, 20, 667}, 17]
CROSSREFS
Sequence in context: A201724 A006410 A159874 * A034404 A179712 A012802
KEYWORD
nonn,easy
AUTHOR
Ant King, Dec 30 2011
STATUS
approved

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Last modified July 24 17:33 EDT 2024. Contains 374585 sequences. (Running on oeis4.)