OFFSET
0,2
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = 2*A134058(n, k) - 1.
From G. C. Greubel, May 03 2021: (Start)
T(n, k) = 4*binomial(n, k) - 2*[n=0] - 1.
Sum_{k=0..n} T(n, k) = 2^(n+2) - (n + 1 + 2*[n=0]) = A095768(n) - 2*[n=0]. (End)
EXAMPLE
First few rows of the triangle are:
1;
3, 3;
3, 7, 3;
3, 11, 11, 3;
3, 15, 23, 15, 3;
3, 19, 39, 39, 19, 3;
3, 23, 59, 79, 59, 23, 3;
...
MATHEMATICA
Table[4*Binomial[n, k] -2*Boole[n==0] -1, {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, May 03 2021 *)
PROG
(Magma) [1] cat [4*Binomial(n, k) -1: k in [0..n], n in [1..12]]; // G. C. Greubel, May 03 2021
(Sage)
def A135087(n, k): return 4*binomial(n, k) -2*bool(n==0) -1
flatten([[A135087(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, May 03 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Nov 18 2007
STATUS
approved