The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A083857 Square array T(n,k) of binomial transforms of generalized Fibonacci numbers, read by ascending antidiagonals, with n, k >= 0. 4
 0, 0, 1, 0, 1, 3, 0, 1, 3, 7, 0, 1, 3, 8, 15, 0, 1, 3, 9, 21, 31, 0, 1, 3, 10, 27, 55, 63, 0, 1, 3, 11, 33, 81, 144, 127, 0, 1, 3, 12, 39, 109, 243, 377, 255, 0, 1, 3, 13, 45, 139, 360, 729, 987, 511, 0, 1, 3, 14, 51, 171, 495, 1189, 2187, 2584, 1023, 0, 1, 3, 15, 57, 205, 648 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS Row n >= 0 of the array gives the solution to the recurrence b(k) = 3*b(k-1) + (n-2) * a(k-2) for k >= 2 with a(0) = 0 and a(1) = 1. These are the binomial transforms of the rows of the generalized Fibonacci numbers A083856. LINKS Table of n, a(n) for n=0..72. OEIS, Transformations of integer sequences. FORMULA T(n, k) = ((3 + sqrt(4*n + 1))/2)^k / sqrt(4*n + 1) - ((3 - sqrt(4*n + 1))/2)^k / sqrt(4*n + 1) for n, k >= 0. O.g.f. of row n >= 0: -x/(-1 + 3*x + (n-2)*x^2) . - R. J. Mathar, Nov 23 2007 T(n,k) = Sum_{i = 0..k} binomial(k,i)*A083856(n,i). - Petros Hadjicostas, Dec 24 2019 EXAMPLE Array T(n,k) (with rows n >= 0 and columns k >= 0) begins as follows: 0, 1, 3, 7, 15, 31, 63, 127, 255, ... 0, 1, 3, 8, 21, 55, 144, 377, 987, ... 0, 1, 3, 9, 27, 81, 243, 729, 2187, ... 0, 1, 3, 10, 33, 109, 360, 1189, 3927, ... 0, 1, 3, 11, 39, 139, 495, 1763, 6279, ... 0, 1, 3, 12, 45, 171, 648, 2457, 9315, ... ... CROSSREFS Rows include A000225 (n=0), A001906 (n=1), A000244 (n=2), A006190 (n=3), A007482 (n=4), A030195 (n=5), A015521 (n=6). Cf. A083856, A083861 (binomial transform), A083862 (main diagonal). Sequence in context: A350178 A248949 A325673 * A353077 A115142 A346203 Adjacent sequences: A083854 A083855 A083856 * A083858 A083859 A083860 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, May 06 2003 EXTENSIONS Various sections edited by Petros Hadjicostas, Dec 24 2019 STATUS approved

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

Last modified September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)