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 A118654 Square array T(n,k) read by antidiagonals: T(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2). 14
 1, 1, 0, 1, 1, 1, 1, 3, 2, 1, 1, 7, 4, 3, 2, 1, 15, 8, 7, 5, 3, 1, 31, 16, 15, 11, 8, 5, 1, 63, 32, 31, 23, 18, 13, 8, 1, 127, 64, 63, 47, 38, 29, 21, 13, 1, 255, 128, 127, 95, 78, 61, 47, 34, 21, 1, 511, 256, 255, 191, 158, 125, 99, 76, 55, 34 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS Inverse binomial transform (by columns) of A090888. LINKS FORMULA T(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2). T(n,k) = (2^n-2)*Fibonacci(k) + Fibonacci(k+1). T(n,0) = 1; T(n,1) = 2^n - 1; T(n,k) = T(n,k-1) + T(n,k-2), for k > 1. T(0,k) = Fibonacci(k-1); T(1,k) = Fibonacci(k+1); T(n,k) = 3T(n-1,k) - 2T(n-2,k), for n > 1. T(n,k) = 2T(n-1,k) + Fibonacci(k-2), for n > 0. T(n,k) = A109754(2^n-2, k+1) = A101220(2^n-2, 0, k+1), for n > 0. O.g.f. (by rows) = (1+(-2+2^n)x)/(1-x-x^2). Sum_{k=0..n} T(n-k,k) = A119587(n+1). - Ross La Haye, May 31 2006 EXAMPLE T(2,3) = 7 because 2^2(Fibonacci(3)) - Fibonacci(3-2) = 4*2 - 1 = 7. {1}; {1,  0}; {1,  1,  1}; {1,  3,  2,  1}; {1,  7,  4,  3,  2}; {1, 15,  8,  7,  5,  3}; {1, 31, 16, 15, 11,  8,  5}; {1, 63, 32, 31, 23, 18, 13,  8}; CROSSREFS Rows: T(0,k) = A000045(k-1), for k > 0; T(1,k) = A000045(k+1); T(2,k) = A000032(k+1); T(3,k) = A022097(k); T(4,k) = A022105(k); T(5,k) = A022401(k). Columns: T(n,1) = A000225(n); T(n,2) = A000079(n); T(n,3) = A000225(n+1); T(n,4) = A055010(n+1); T(n,5) = A051633(n); a(T,6) = A036563(n+3). Sequence in context: A259786 A254410 A073201 * A111760 A078424 A291117 Adjacent sequences:  A118651 A118652 A118653 * A118655 A118656 A118657 KEYWORD nonn,tabl AUTHOR Ross La Haye, May 17 2006 STATUS approved

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Last modified April 18 02:38 EDT 2021. Contains 343072 sequences. (Running on oeis4.)