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

Author

Gary W. Adamson, Dec 06 2006

Keywords

• nonn
• tabl

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, ...).

Examples

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

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.

Crossrefs

Cf. A125714, A125750, A125752.

Extensions

More terms from Joshua Zucker, Jun 17 2007

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