The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A111006 Another version of Fibonacci-Pascal triangle A037027. 15
 1, 0, 1, 0, 1, 2, 0, 0, 2, 3, 0, 0, 1, 5, 5, 0, 0, 0, 3, 10, 8, 0, 0, 0, 1, 9, 20, 13, 0, 0, 0, 0, 4, 22, 38, 21, 0, 0, 0, 0, 1, 14, 51, 71, 34, 0, 0, 0, 0, 0, 5, 40, 111, 130, 55, 0, 0, 0, 0, 0, 1, 20, 105, 233, 235, 89, 0, 0, 0, 0, 0, 0, 6, 65, 256, 474, 420, 144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Triangle T(n,k), 0 <= k <= n, read by rows, given by [0, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...] DELTA [1, 1, -1, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938. Row sums are the Jacobsthal numbers A001045(n+1) and column sums form Pell numbers A000129. Maximal column entries: A038149 = {1, 1, 2, 5, 10, 22, ...}. T(n,k) gives a convolved Fibonacci sequence (A001629, A001872, ...). Triangle read by rows: T(n,n-k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= floor(n/2)). - Philippe Deléham, Feb 17 2014 Diagonal sums are A013979(n). - Philippe Deléham, Feb 17 2014 T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and 1 X 2 tiles. - Emeric Deutsch, Aug 14 2014 LINKS Reinhard Zumkeller, Rows n = 0..120 of table, flattened FORMULA T(0, 0) = 1, T(n, k) = 0 for k < 0 or for n < k, T(n, k) = T(n-1, k-1) + T(n-2, k-1) + T(n-2, k-2). T(n, k) = A037027(k, n-k). T(n, n) = A000045(n+1). T(3n, 2n) = (n+1)*A001002(n+1) = A038112(n). G.f.: 1/(1-yx(1-x)-x^2*y^2). - Paul Barry, Oct 04 2005 Sum_{k=0..n} x^k*T(n,k) = (-1)^n*A053524(n+1), (-1)^n*A083858(n+1), (-1)^n*A002605(n), A033999(n), A000007(n), A001045(n+1), A083099(n) for x = -4, -3, -2, -1, 0, 1, 2 respectively. - Philippe Deléham, Dec 02 2006 Sum_{k=0..n} T(n,k)*x^(n-k) = A053404(n), A015447(n), A015446(n), A015445(n), A015443(n), A015442(n), A015441(n), A015440(n), A006131(n), A006130(n), A001045(n+1), A000045(n+1) for x = 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 respectively. - Philippe Deléham, Feb 17 2014 EXAMPLE Triangle begins:   1;   0, 1;   0, 1, 2;   0, 0, 2, 3;   0, 0, 1, 5,  5;   0, 0, 0, 3, 10,  8;   0, 0, 0, 1,  9, 20, 13;   0, 0, 0, 0,  4, 22, 38,  21;   0, 0, 0, 0,  1, 14, 51,  71,  34;   0, 0, 0, 0,  0,  5, 40, 111, 130,  55;   0, 0, 0, 0,  0,  1, 20, 105, 233, 235,  89;   0, 0, 0, 0,  0,  0,  6,  65, 256, 474, 420, 144; PROG (Haskell) a111006 n k = a111006_tabl !! n !! k a111006_row n = a111006_tabl !! n a111006_tabl =  map fst \$ iterate (\(us, vs) ->    (vs, zipWith (+) (zipWith (+) ([0] ++ us ++ [0]) ([0, 0] ++ us))                     ([0] ++ vs))) ([1], [0, 1]) -- Reinhard Zumkeller, Aug 15 2013 CROSSREFS Cf. A000045, A000129, A001045, A037027, A038112, A038149, A084938, A128100 (reversed version). Some other Fibonacci-Pascal triangles: A027926, A036355, A037027, A074829, A105809, A109906, A114197, A162741, A228074. Sequence in context: A122908 A296441 A091008 * A046742 A263138 A274637 Adjacent sequences:  A111003 A111004 A111005 * A111007 A111008 A111009 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Oct 02 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 20 23:28 EDT 2020. Contains 337910 sequences. (Running on oeis4.)