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A125751 A Moessner triangle using (1, 2, 1, 2, 1, 2, ...). 3
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A209153 A209141 A038719 * A210860 A099492 A359708
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

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Last modified July 19 16:24 EDT 2024. Contains 374410 sequences. (Running on oeis4.)