

A054888


Layer counting sequence for hyperbolic tessellation by regular pentagons of angle Pi/2.


16



1, 5, 15, 40, 105, 275, 720, 1885, 4935, 12920, 33825, 88555, 231840, 606965, 1589055, 4160200, 10891545, 28514435, 74651760, 195440845, 511670775, 1339571480, 3507043665, 9181559515, 24037634880, 62931345125
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OFFSET

1,2


COMMENTS

The layer sequence is the sequence of the cardinalities of the layers accumulating around a (finitesided) polygon of the tessellation under successive sidereflections.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Illustration
Index entries for linear recurrences with constant coefficients, signature (3,1).


FORMULA

G.f.: (1+x)^2/(x^23*x+1).
G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^2 * x^n/n ). [Paul D. Hanna, Feb 21 2012]
a(n) = A001906(n1)+2*A001906(n)+A001906(n+1).  R. J. Mathar, Nov 28 2011
a(n) = A203976(A004277(n1)). [Reinhard Zumkeller, Jan 11 2012]
a(n) = 5*A000045(2*n) for n >= 1.  Robert Israel, Jun 01 2015


PROG

(Haskell)
a054888 n = a054888_list !! (n1)
a054888_list = 1 : zipWith (+) (tail a002878_list) a002878_list
 Reinhard Zumkeller, Jan 11 2012
(PARI) {a(n)=polcoeff(exp(sum(k=1, n, 5*fibonacci(k)^2*x^k/k)+x*O(x^n)), n)} /* Paul D. Hanna, Feb 21 2012 */


CROSSREFS

{a(n)/5} for n>1 is A001906.
Cf. A002878.
Sequence in context: A152881 A000333 A291225 * A201157 A301980 A230955
Adjacent sequences: A054885 A054886 A054887 * A054889 A054890 A054891


KEYWORD

nonn,easy


AUTHOR

Paolo Dominici (pl.dm(AT)libero.it), May 23 2000


STATUS

approved



