

A203135


Indices of hexagonal numbers that are also decagonal


2



1, 28, 943, 32026, 1087933, 36957688, 1255473451, 42649139638, 1448815274233, 49217070184276, 1671931570991143, 56796456343514578, 1929407584108504501, 65543061403345638448, 2226534680129643202723, 75636636063004523254126, 2569419091462024147437553
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OFFSET

1,2


COMMENTS

As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^4=17+12*sqrt(2).


LINKS

Table of n, a(n) for n=1..17.
Index entries for linear recurrences with constant coefficients, signature (35, 35, 1).


FORMULA

G.f.: x(17*x2*x^2) / ((1x)*(134*x+x^2))
a(n) = 35*a(n1)35*a(n2)+a(n3)
a(n) = 34*a(n1)a(n2)8
a(n) = 1/16 *((3*sqrt(2)2)*(1+sqrt(2))^(4*n2) (3*sqrt(2)+2)*(1sqrt(2))^(4*n2)+4)
a(n) = ceiling(1/16 *(3*sqrt(2)2)*(1+sqrt(2))^(4*n2))


EXAMPLE

The second hexagonal number which is also decagonal is A000384(28)=1540. Hence a(2) = 28.


MATHEMATICA

LinearRecurrence[{35, 35, 1}, {1, 28, 943}, 17]


CROSSREFS

Cf. A203134, A203136, A000384, A001107.
Sequence in context: A160263 A129461 A239336 * A097579 A091549 A034904
Adjacent sequences: A203132 A203133 A203134 * A203136 A203137 A203138


KEYWORD

nonn,easy


AUTHOR

Ant King, Dec 30 2011


STATUS

approved



