login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..65.

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

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

License Agreements, Terms of Use, Privacy Policy .

Last modified August 21 23:23 EDT 2017. Contains 290940 sequences.