A048900 Heptagonal pentagonal numbers.

1, 4347, 16701685, 64167869935, 246532939589097, 947179489733441251, 3639063353022941697757, 13981280455134652269341655, 53716075869563980995868941265, 206377149509584359851476202998987, 792900954699747240985390576053167301

Offset

1,2

Comments

As n increases, this sequence is approximately geometric with common ratio r=lim(n->Infinity,a(n)/a(n-1))=(4+sqrt(15))^4=1921+496*sqrt(15). - Ant King, Dec 15 2011

Links

Colin Barker, Table of n, a(n) for n = 1..279

Eric Weisstein's World of Mathematics, Heptagonal Pentagonal Number.

Index entries for linear recurrences with constant coefficients, signature (3843,-3843,1).

Formula

From Ant King, Dec 15 2011: (Start)

a(n) = 3843*a(n-1) - 3843*a(n-2) + a(n-3).

a(n) = 3842*a(n-1) - a(n-2) + 512.

a(n) = 1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3)+ (2-sqrt(15))^2*(4-sqrt(15))^(4n-3)-32).

a(n) = floor(1/240*((2+sqrt(15))^2*(4+sqrt(15))^(4n-3))).

G.f.: x*(1+504*x+7*x^2)/((1-x)*(1-3842*x+x^2)).

(End)

Mathematica

LinearRecurrence[{3843, -3843, 1}, {1, 4347, 16701685}, 10] (* Ant King, Dec 15 2011 *)

Prog

(PARI) Vec(-x*(7*x^2+504*x+1)/((x-1)*(x^2-3842*x+1)) + O(x^30)) \\ Colin Barker, Jun 23 2015

Crossrefs

Cf. A046198, A046199.

Sequence in context: A252431 A251947 A145916 * A294985 A252302 A235066

Adjacent sequences: A048897 A048898 A048899 * A048901 A048902 A048903

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved