OFFSET
1,2
COMMENTS
Row sums are s(n) = 1, 4, 11, 28, 69, 167, 400, ...
Binomial transform of the bidiagonal matrix with (1,2,3...) in the main diagonal and the Fibonacci numbers (1,1,2,3,5,8,...) in the subdiagonal.
FORMULA
T(n,2) = A000096(n-1).
T(n,3) = A051925(n-1).
T(n,4) = A215862(n-3). - R. J. Mathar, Aug 10 2013
Row sums s(n) = 7*s(n-1) -17*s(n-2) +16*s(n-3) -4*s(n-4) with s(n) = A001787(n+1)/4 +A001906(n-1). - R. J. Mathar, Aug 10 2013
EXAMPLE
First few rows of the triangle:
1;
2, 2;
3, 5, 3;
4, 9, 11, 4;
5, 14, 26, 19, 5;
6, 20, 50, 55, 30, 6;
7, 27, 85, 125, 105, 44, 7;
8, 35, 133, 245, 280, 182, 62, 8;
...
MAPLE
with(combinat): T:=(n, k)->k*binomial(n-1, k-1)+fibonacci(k)*binomial(n-1, k): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
MATHEMATICA
Flatten[Table[k Binomial[n-1, k-1]+Fibonacci[k]Binomial[n-1, k], {n, 15}, {k, n}]] (* Harvey P. Dale, Nov 03 2014 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 20 2006
EXTENSIONS
Edited by N. J. A. Sloane, Nov 29 2006
STATUS
approved