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A048902 Indices of heptagonal numbers (A000566) which are also hexagonal. 3
1, 221, 71065, 22882613, 7368130225, 2372515049741, 763942477886281, 245987105364332645, 79207083984837225313, 25504435056012222218045, 8212348880951950716985081, 2644350835231472118646977941 (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(5))^4 = 161 + 72*sqrt(5). - Ant King, Dec 26 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Heptagonal hexagonal number.

Index entries for linear recurrences with constant coefficients, signature (323,-323,1).

FORMULA

G.f.: -x*(1 - 102*x + 5*x^2) / ( (x-1)*(x^2 - 322*x + 1) ). - R. J. Mathar, Dec 21 2011

From Ant King, Dec 26 2011: (Start)

a(n) = 322*a(n-1) - a(n-2) - 96.

a(n) = (1/20)*((sqrt(5)+1)*(sqrt(5)+2)^(4*n-3) + (sqrt(5)-1)*(sqrt(5)-2)^(4*n-3) + 6).

a(n) = ceiling((1/20)*(sqrt(5)+1)*(sqrt(5)+2)^(4*n-3)).

(End)

MATHEMATICA

LinearRecurrence[{323, -323, 1}, {1, 221, 71065}, 12]; (* Ant King, Dec 26 2011 *)

PROG

(MAGMA) I:=[1, 221, 71065]; [n le 3 select I[n] else 323*Self(n-1)-323*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 28 2011

CROSSREFS

Cf. A048901, A048903.

Sequence in context: A220737 A220723 A011816 * A210135 A013548 A300517

Adjacent sequences:  A048899 A048900 A048901 * A048903 A048904 A048905

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified January 27 15:07 EST 2022. Contains 350607 sequences. (Running on oeis4.)