A203134 Decagonal hexagonal numbers

1, 1540, 1777555, 2051297326, 2367195337045, 2731741367653000, 3152427171076225351, 3637898223680596402450, 4198131397700237172202345, 4844639995047850016125104076, 5590710356153821218371197901755, 6451674906361514638150346253521590

Offset

1,2

Comments

As n increases, this sequence is approximately geometric with common ratio (1+sqrt(2))^8 = 577+408*sqrt(2).

Links

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

Index entries for linear recurrences with constant coefficients, signature (1155, -1155, 1).

Formula

G.f.: x*(1+385*x+10*x^2) / ((1-x)*(1-1154*x+x^2)).

a(n) = 1155*a(n-1)-1155*a(n-2)+a(n-3).

a(n) = 1154*a(n-1)-a(n-2)+396.

a(n) = (1/64)*((5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)+ (5*sqrt(2)+1)*(sqrt(2)-1)^(8*n-5)-22).

a(n) = floor(1/64 *(5*sqrt(2)-1)*(sqrt(2)+1)^(8*n-5)).

Example

The second number which is both hexagonal and decagonal is 1540. Hence a(2) = 1540.

Mathematica

LinearRecurrence[{1155, -1155, 1}, {1, 1540, 1777555}, 12]

Crossrefs

Cf. A203135, A203136, A000384, A001107.

Sequence in context: A237400 A200429 A092717 * A083734 A137598 A252966

Adjacent sequences: A203131 A203132 A203133 * A203135 A203136 A203137

Keyword

nonn,easy

Author

Ant King, Dec 30 2011

Status

approved