OFFSET
0,5
COMMENTS
First row just gives the tribonacci numbers.
n offset is 0 but d offset is 1 so 1st entry is a(1,0).
LINKS
G. C. Greubel, Table of n, a(n) for the first 25 rows, flattened
FORMULA
a(d,n) = Product_{i=0 to d-1} T(floor(n + i)/d) + 2) where T is the n-th tribonacci number.
EXAMPLE
1, 2, 4, 7, 13, 24, 44, 81, 149, 274, 504, ...
1, 2, 4, 8, 16, 28, 49, 91, 169, 312, 576, ...
1, 2, 4, 8, 16, 32, 64, 112, 196, 343, 637, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 448, 784, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, ...
................................................
For a(2,5) we count subsets of {1,...,5} that do not contain {1,3,5}, the only d=2 AP possible here. There are 4 subsets containing {1,3,5} so a(2,5) = 2^5-4 = 28.
MATHEMATICA
T[0] = 0; T[1] = 1; T[2] = 1; T[n_] := T[n - 1] + T[n - 2] + T[n - 3]; a[d_, n_] := Product[T[Floor[(n + i)/d] + 2], {i, 0, d - 1}]; Flatten[Table[a[j, i - j], {i, 0, 10}, {j, 0, i}]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
David Nacin, Mar 09 2012
STATUS
approved