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%I M1435 #48 Feb 16 2025 08:32:28
%S 1,2,5,13,33,81,193,449,1089,2673,6561,15633,37249,88209,216513,
%T 531441,1266273,3017169,7189057,17537553,43046721,102568113,244390689,
%U 582313617,1420541793,3486784401,8308017153,19795645809,47167402977,115063885233,282429536481
%N Number of ways to add n ordinals.
%D W. Sierpiński, Cardinal and Ordinal Numbers, 2nd ed. p 275.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. Erdős, <a href="http://dx.doi.org/10.1090/S0002-9939-1950-0035809-8">Some remarks on set theory</a>, Proc. Am. Math. Soc. 1 (1950) 127-141.
%H R. K. Guy, <a href="http://www.jstor.org/stable/2691503">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20.
%H R. K. Guy, <a href="/A005347/a005347.pdf">The Second Strong Law of Small Numbers</a>, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
%H R. K. Guy and N. J. A. Sloane, <a href="/A005180/a005180.pdf">Correspondence</a>, 1988.
%H Bill Sands and Tommy Kucera, <a href="/A005348/a005348.pdf">Letter to N. J. A. Sloane</a>, Jun 10 1975.
%H A. Wakulicz, <a href="http://matwbn.icm.edu.pl/ksiazki/fm/fm36/fm36126.pdf">Sur la somme d'un nombre fini de nombres ordinaux</a>, Fund. Math. 36 (1949), 254-266.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OrdinalNumber.html">Ordinal Number</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,81).
%F a(n) = 81*a(n-5) for n >= 21.
%t Join[{1, 2, 5, 13, 33, 81, 193, 449, 1089, 2673, 6561, 15633, 37249, 88209}, LinearRecurrence[ {0, 0, 0, 0, 81}, {216513, 531441, 1266273, 3017169, 7189057}, 20]] (* _Harvey P. Dale_, Dec 15 2014 *)
%o (Magma) I:=[1,2,5,13,33,81,193,449,1089,2673,6561,15633,37249, 88209,216513,531441,1266273,3017169,7189057,17537553, 43046721]; [n le 21 select I[n] else 81*Self(n-5): n in [1..50]]; // _Vincenzo Librandi_, Dec 17 2015
%K nonn,easy,changed
%O 1,2
%A _N. J. A. Sloane_, _R. K. Guy_, Bill Sands and Tommy Kucera