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A131301
Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.
3
1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 4, 7, 1, 1, 1, 7, 7, 10, 1, 1, 1, 7, 16, 10, 13, 1, 1, 1, 10, 16, 28, 13, 16, 1, 1, 1, 10, 28, 28, 43, 16, 19, 1, 1, 1, 13, 28, 58, 43, 61, 19, 22, 1, 1, 1, 13, 43, 58, 103, 61, 82, 22, 25, 1, 1, 1, 16, 43, 103, 103, 166, 82
OFFSET
0,8
COMMENTS
Row sums = A131300: (1, 2, 3, 7, 14, 27, 49, 86, ...). Reversed triangle = A131299.
LINKS
Nathaniel Johnston, Rows 0..100, flattened
FORMULA
3*A046854 - 2*A000012 as infinite lower triangular matrices (former name).
T(n,k) = 3*binomial(floor((n+k)/2),k)-2. - Nathaniel Johnston, Jun 29 2011
EXAMPLE
First few rows of the triangle:
1;
1, 1;
1, 1, 1;
1, 4, 1, 1;
1, 4, 7, 1, 1;
1, 7, 7, 10, 1, 1;
1, 7, 16, 10, 13, 1, 1;
...
MAPLE
for n from 0 to 6 do seq(3*binomial(floor((n+k)/2), k)-2, k=0..n); od; # Nathaniel Johnston, Jun 29 2011
MATHEMATICA
t[n_, k_] := 3 Binomial[Floor[(n + k)/2], k] - 2; Table[t[n, k], {n, 11}, {k, 0, n}] // Flatten
(* to view triangle: Table[t[n, k], {n, 5}, {k, 0, n}] // TableForm *) (* Robert G. Wilson v, Feb 28 2015 *)
CROSSREFS
KEYWORD
nonn,easy,tabl
AUTHOR
Gary W. Adamson, Jun 27 2007
STATUS
approved