A125751 A Moessner triangle using (1, 2, 1, 2, 1, 2, ...).

1, 2, 1, 4, 5, 2, 10, 18, 9, 2, 38, 78, 53, 15, 1, 186, 422, 344, 129, 23, 1, 1106, 2704, 2484, 1123, 268, 32, 2, 7718, 19998, 20080, 10342, 2991, 490, 42, 2, 61662, 167520, 180466, 102700, 34211, 6891, 824, 54, 1, 554330, 1567518, 1789474, 1103206

Offset

1,2

Comments

Circle terms n = 1, 3, 6, 10, ... in the sequence (1, 2, 1, 2, 1, 2, ...). Partial sums of the uncircled terms becomes row 2. Circle the terms in row 2 that are one place offset to the left of the circled row 1 terms. Take partial sums and continue with analogous operations. (Cf. A125714 and "The Book of Numbers", p. 64.)

Left border (1, 2, 4, 10, 38, 186, 1106, 7718, 61662, ...).

References

J. H. Conway and R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 64.

Links

Joshua Zucker, Table of n, a(n) for n = 1..65

G. S. Kazandzidis, On a conjecture of Moessner and a general problem, Bull. Soc. Math. Grèce (N.S.) 2 (1961), 23-30.

Dexter Kozen and Alexandra Silva, On Moessner's theorem, Amer. Math. Monthly 120(2) (2013), 131-139.

Calvin T. Long, Strike it out--add it up, Math. Gaz. 66 (438) (1982), 273-277.

Alfred Moessner, Eine Bemerkung über die Potenzen der natürlichen Zahlen, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 29, 1951.

Oskar Perron, Beweis des Moessnerschen Satzes, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 31-34, 1951.

Example

First few rows of the triangle are:
   1;
   2,  1;
   4,  5,  2;
  10, 18,  9,  2;
  38, 78, 53, 15,  1;
  ...

Crossrefs

Cf. A125714, A125750, A125752.

Sequence in context: A209153 A209141 A038719 * A210860 A099492 A359708

Adjacent sequences: A125748 A125749 A125750 * A125752 A125753 A125754

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 06 2006

Extensions

More terms from Joshua Zucker, Jun 17 2007

Corrected the comment concerning the left border - R. J. Mathar, Sep 17 2009

Status

approved