cp's OEIS Frontend

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

%I A125751 #29 Aug 10 2019 18:44:35
%S A125751 1,2,1,4,5,2,10,18,9,2,38,78,53,15,1,186,422,344,129,23,1,1106,2704,
%T A125751 2484,1123,268,32,2,7718,19998,20080,10342,2991,490,42,2,61662,167520,
%U A125751 180466,102700,34211,6891,824,54,1,554330,1567518,1789474,1103206
%N A125751 A Moessner triangle using (1, 2, 1, 2, 1, 2, ...).
%C A125751 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.)
%C A125751 Left border (1, 2, 4, 10, 38, 186, 1106, 7718, 61662, ...).
%D A125751 J. H. Conway and R. K. Guy, "The Book of Numbers", Springer-Verlag, 1996, p. 64.
%H A125751 Joshua Zucker, <a href="/A125751/b125751.txt">Table of n, a(n) for n = 1..65</a>
%H A125751 G. S. Kazandzidis, <a href="http://www.hms.gr/apothema/?s=sap&amp;i=20">On a conjecture of Moessner and a general problem</a>, Bull. Soc. Math. Grèce (N.S.) 2 (1961), 23-30.
%H A125751 Dexter Kozen and Alexandra Silva, <a href="https://www.jstor.org/stable/10.4169/amer.math.monthly.120.02.131">On Moessner's theorem</a>, Amer. Math. Monthly 120(2) (2013), 131-139.
%H A125751 Calvin T. Long, <a href="https://doi.org/10.2307/3615513">Strike it out--add it up</a>, Math. Gaz. 66 (438) (1982), 273-277.
%H A125751 Alfred Moessner, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1951_0029.pdf">Eine Bemerkung über die Potenzen der natürlichen Zahlen</a>, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 29, 1951.
%H A125751 Oskar Perron, <a href="https://www.zobodat.at/pdf/Sitz-Ber-Akad-Muenchen-math-Kl_1951_0031-0034.pdf">Beweis des Moessnerschen Satzes</a>, S.-B. Math.-Nat. Kl. Bayer. Akad. Wiss., 31-34, 1951.
%e A125751 First few rows of the triangle are:
%e A125751    1;
%e A125751    2,  1;
%e A125751    4,  5,  2;
%e A125751   10, 18,  9,  2;
%e A125751   38, 78, 53, 15,  1;
%e A125751   ...
%Y A125751 Cf. A125714, A125750, A125752.
%K A125751 nonn,tabl
%O A125751 1,2
%A A125751 _Gary W. Adamson_, Dec 06 2006
%E A125751 More terms from _Joshua Zucker_, Jun 17 2007
%E A125751 Corrected the comment concerning the left border - _R. J. Mathar_, Sep 17 2009