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A054888
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Layer counting sequence for hyperbolic tessellation by regular pentagons of angle Pi/2.
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17
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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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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: (1+x)^2/(1-3*x+x^2).
G.f.: exp( Sum_{n>=1} 5*Fibonacci(n)^2 * x^n/n ). - Paul D. Hanna, Feb 21 2012
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MATHEMATICA
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LinearRecurrence[{3, -1}, {1, 5, 15}, 30] (* Harvey P. Dale, Jan 15 2023 *)
Join[{1}, 5*Fibonacci[2*Range[40]]] (* G. C. Greubel, Feb 08 2023 *)
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PROG
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(Haskell)
a054888 n = a054888_list !! (n-1)
a054888_list = 1 : zipWith (+) (tail a002878_list) a002878_list
(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 */
(Magma) [n eq 0 select 1 else 5*Fibonacci(2*n): n in [0..40]]; // G. C. Greubel, Feb 08 2023
(SageMath) [5*fibonacci(2*n) + int(n==0) for n in range (41)] # G. C. Greubel, Feb 08 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Paolo Dominici (pl.dm(AT)libero.it), May 23 2000
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EXTENSIONS
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STATUS
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approved
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