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A203629 Indices of 10-gonal (decagonal) numbers which are also 9-gonal (nonagonal). 2
1, 551, 494461, 444025091, 398734036921, 358062721129631, 321539924840371381, 288742494443932370171, 259290438470726428041841, 232842525004217888449202711, 209092328163349193100955992301, 187764677848162571186770031883251 (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->Infinity, a(n)/a(n-1)) = (2*sqrt(2)+sqrt(7))^4 = 449+120*sqrt(14).

LINKS

Table of n, a(n) for n=1..12.

Index entries for linear recurrences with constant coefficients, signature (899, -899, 1).

FORMULA

G.f.: x*(1-348*x+11*x^2) / ((1-x)*(1-898*x+x^2)).

a(n) = 898*a(n-1)-a(n-2)-336.

a(n) = 899*a(n-1)-899*a(n-2)+a(n-3).

a(n) = 1/112*((sqrt(7)+7*sqrt(2))*(2*sqrt(2)+sqrt(7))^(4*n-3)-(sqrt(7)-7*sqrt(2))*(2*sqrt(2)-sqrt(7))^(4*n-3)+42).

a(n) = ceiling(1/112*(sqrt(7)+7*sqrt(2))*(2*sqrt(2)+sqrt(7))^(4*n-3)).

EXAMPLE

The second number that is both 9-gonal (nonagonal) and 10-gonal (decagonal) is A001107(551) = 1212751. Hence a(2) = 551.

MATHEMATICA

LinearRecurrence[{899, -899, 1}, {1, 551, 494461}, 12]

CROSSREFS

Cf. A203627, A203628, A001107, A001106.

Sequence in context: A063877 A204870 A263947 * A119897 A014360 A158636

Adjacent sequences:  A203626 A203627 A203628 * A203630 A203631 A203632

KEYWORD

nonn,easy

AUTHOR

Ant King, Jan 06 2012

STATUS

approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)