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A202565 Indices of decagonal numbers which are also pentagonal. 2
1, 56, 5451, 534106, 52336901, 5128482156, 502538914351, 49243685124206, 4825378603257801, 472837859434140256, 46333284845942487251, 4540189077042929610306, 444892196265361159322701, 43594895044928350684014356, 4271854822206713005874084151 (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(3)+sqrt(2))^4 = 49+20*sqrt(6).
LINKS
FORMULA
G.f.: x*(1-43*x+6*x^2) / ((1-x)*(1-98*x+x^2)).
a(n) = 98*a(n-1)-a(n-2)-36.
a(n) = 99*a(n-1)-99*a(n-2)+a(n-3).
a(n) = 1/48*(5*sqrt(3)*((sqrt(3)+sqrt(2))^(4n-3)+(sqrt(3)-sqrt(2))^(4n-3))+18).
a(n) = ceiling(5/48*sqrt(3)*(sqrt(3)+sqrt(2))^(4n-3)).
EXAMPLE
The second decagonal number that is also pentagonal is A001107(56) = 12376. Hence a(2)=56.
MATHEMATICA
LinearRecurrence[{99, -99, 1}, {1, 56, 5451}, 15]
CROSSREFS
Sequence in context: A278324 A009600 A278777 * A213693 A180372 A255960
KEYWORD
nonn,easy
AUTHOR
Ant King, Dec 22 2011
STATUS
approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)