A005348 Number of ways to add n ordinals. (Formerly M1435)

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

1,2

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

Table of n, a(n) for n=1..31.

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 * A369578 A210496 A067676

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