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 A005348 Number of ways to add n ordinals. (Formerly M1435) 3
 1, 2, 5, 13, 33, 81, 193, 449, 1089, 2673, 6561, 15633, 37249, 88209, 216513, 531441, 1266273, 3017169, 7189057, 17537553, 43046721, 102568113, 244390689, 582313617, 1420541793, 3486784401, 8308017153, 19795645809, 47167402977, 115063885233, 282429536481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES W. Sierpiński, Cardinal and Ordinal Numbers, 2nd ed. p 275. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS P. Erdős, Some remarks on set theory, Proc. Am. Math. Soc. 1 (1950) 127-141. R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy] R. K. Guy and N. J. A. Sloane, Correspondence, 1988. Bill Sands and Tommy Kucera, Letter to N. J. A. Sloane, Jun 10 1975. A. Wakulicz, Sur la somme d'un nombre fini de nombres ordinaux, Fund. Math. 36 (1949), 254-266. Eric Weisstein's World of Mathematics, Ordinal Number Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,81). FORMULA a(n) = 81*a(n-5) for n >= 21. MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A001659 A088921 A005183 * A210496 A067676 A292507 Adjacent sequences:  A005345 A005346 A005347 * A005349 A005350 A005351 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, R. K. Guy, Bill Sands and Tommy Kucera STATUS approved

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Last modified October 22 12:22 EDT 2018. Contains 316446 sequences. (Running on oeis4.)