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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The layer sequence is the sequence of the cardinalities of the layers accumulating around a (finite-sided) polygon of the tessellation under successive side-reflections.

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^2-3*x+1).

G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^2 * x^n/n ). [Paul D. Hanna, Feb 21 2012]

a(n) = A001906(n-1)+2*A001906(n)+A001906(n+1). - R. J. Mathar, Nov 28 2011

a(n) = A203976(A004277(n-1)). [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 !! (n-1)

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

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Last modified December 12 09:36 EST 2019. Contains 329953 sequences. (Running on oeis4.)