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 A083856 Square array of generalized Fibonacci numbers, read by antidiagonals. 8
 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 3, 1, 0, 1, 1, 4, 5, 5, 1, 0, 1, 1, 5, 7, 11, 8, 1, 0, 1, 1, 6, 9, 19, 21, 13, 1, 0, 1, 1, 7, 11, 29, 40, 43, 21, 1, 0, 1, 1, 8, 13, 41, 65, 97, 85, 34, 1, 0, 1, 1, 9, 15, 55, 96, 181, 217, 171, 55, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,14 COMMENTS Array gives solutions to the recurrences a(n)=a(n-1)+ka(n-2),a(0)=0,a(1)=1,k>=0. Rows include A000045, A001045, A006130, A006131, A015440, A015441, A015441, A015442, A015443, A015445. LINKS FORMULA T(n, k)=(1+(sqrt(4k+1))/2)^n/sqrt(4k+1)-((1-sqrt(4k+1))/2)^n/sqrt(4k+1) EXAMPLE Rows begin 0 1 1 1 1 1 ... 0 1 1 2 3 5 ... 0 1 1 3 5 11 ... 0 1 1 4 7 19 ... 0 1 1 5 9 29 ... CROSSREFS Cf. A083857. Sequence in context: A133607 A103631 A192517 * A081718 A198062 A129634 Adjacent sequences:  A083853 A083854 A083855 * A083857 A083858 A083859 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, May 06 2003 STATUS approved

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