A005348 Number of ways to add n ordinals.

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

Offset: 1

Author

N. J. A. Sloane, R. K. Guy, Bill Sands and Tommy Kucera

Keywords

• nonn
• easy

References

• John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 270-271.
• 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).

Programs

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

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 *)

Formula

a(n) = 81*a(n-5) for n >= 21.