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 A162997 Array A(n,k) read by antidiagonals downward (n >= 0, k >= 1): the bottom-right element of the 2 X 2 matrix [1,n; 1,n+1] raised to k-th power. 6
 1, 1, 2, 1, 5, 3, 1, 13, 11, 4, 1, 34, 41, 19, 5, 1, 89, 153, 92, 29, 6, 1, 233, 571, 436, 169, 41, 7, 1, 610, 2131, 2089, 985, 281, 55, 8, 1, 1597, 7953, 10009, 5741, 1926, 433, 71, 9 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS With k=0 column added, becomes A094954. Also, A(n,k) is the top-left element of the same 2 X 2 matrix raised to (k+1)-th power. Also, A(n,k) is the denominator of the rational number which has continued fraction expansion consisting of k repeats of [1, n]. Example: the row (3, 11, 41, ...) is extracted from denominators of the continued fractions [0; 1, 2], [0; 1, 2, 1, 2], ... = 2/3, 8/11, ... Also, A(n,k)=Product_{i=1..k} (n+2+2*cos(2*Pi*i/(2*k+1))). This is somehow connected to the diagonal product formulas for (2*k+1)-gons found by Steinbach. Row sums of the triangle = A162998: (1, 3, 29, 100, 369, 1458, ...). LINKS P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31. EXAMPLE The array begins: 1,...1,...1,....1,....1,.....1,.....1,... 2,...5,..13,...34,...89,...233....610,... 3,..11,..41,..153,..571,..2131,.......... 4,..19,..91,..436,.2089,................. 5,..29,.169,..985,....................... 6,..41,.281,............................. 7,..55,.................................. 8,....................................... ... CROSSREFS Cf. A028387, A094954, A162988, A152063. Sequence in context: A048472 A038622 A193954 * A112339 A132808 A135233 Adjacent sequences:  A162994 A162995 A162996 * A162998 A162999 A163000 KEYWORD nonn,tabl AUTHOR Gary W. Adamson, Jul 19 2009 EXTENSIONS Spelling corrected by Jason G. Wurtzel, Aug 22 2010 Edited by Andrey Zabolotskiy, Sep 18 2017 STATUS approved

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Last modified October 22 09:57 EDT 2018. Contains 316433 sequences. (Running on oeis4.)