A134082 Triangle read by rows, (n-1) zeros followed by (2n, 1).
1, 2, 1, 0, 4, 1, 0, 0, 6, 1, 0, 0, 0, 8, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 0, 0, 14, 1, 0, 0, 0, 0, 0, 0, 0, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 18, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 24, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 1
Offset: 0
Examples
First few rows of the triangle: 1; 2, 1; 0, 4, 1; 0, 0, 6, 1; 0, 0, 0, 8, 1; 0, 0, 0, 0, 10, 1; ...
Links
- G. C. Greubel, Rows n = 0..50 of the triangle, flattened
Programs
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Magma
A134082:= func< n,k | k eq n select 1 else k eq n-1 select 2*n else 0 >; [A134082(n,k): k in [0..n], n in [0..15]]; // G. C. Greubel, Feb 17 2021
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Mathematica
T[n_, k_]:= If[k==n, 1, If[k==n-1, 2*n, 0]]; Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* G. C. Greubel, Feb 17 2021 *) -
Sage
def A134082(n,k): return 1 if k==n else 2*n if k==n-1 else 0 flatten([[A134082(n,k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Feb 17 2021
Formula
Triangle read by rows, (n-1) zeros followed by (2n, 1). As an infinite lower triangular matrix, (1,1,1,...) in the main diagonal and (2,4,6,8,...) in the subdiagonal.
From formalism in A132382, e.g.f. = I_o[2*(u*x)^(1/2)] (1+2x) where I_o is the zeroth modified Bessel function of the first kind, i.e., I_o[2*(u*x)^(1/2)] = Sum_{j>=0} u^j/j! * x^j/j!. - Tom Copeland, Dec 07 2007
Row polynomial e.g.f.: exp(x*y)(1+2x). - Tom Copeland, Dec 03 2013
Sum_{k=0..n} T(n,k) = 2*n+1 = A005408(n). - G. C. Greubel, Feb 17 2021
Extensions
More terms added by G. C. Greubel, Feb 17 2021
Comments