login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A336820 A(n,k) is the n-th number that is a sum of at most k positive k-th powers; square array A(n,k), n>=1, k>=1, read by antidiagonals. 12
0, 0, 1, 0, 1, 2, 0, 1, 2, 3, 0, 1, 2, 4, 4, 0, 1, 2, 3, 5, 5, 0, 1, 2, 3, 8, 8, 6, 0, 1, 2, 3, 4, 9, 9, 7, 0, 1, 2, 3, 4, 16, 10, 10, 8, 0, 1, 2, 3, 4, 5, 17, 16, 13, 9, 0, 1, 2, 3, 4, 5, 32, 18, 17, 16, 10, 0, 1, 2, 3, 4, 5, 6, 33, 19, 24, 17, 11, 0, 1, 2, 3, 4, 5, 6, 64, 34, 32, 27, 18, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,6
LINKS
FORMULA
A(n,k) = n-1 for n <= k+1.
EXAMPLE
Square array A(n,k) begins:
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ...
3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, ...
4, 5, 8, 4, 4, 4, 4, 4, 4, 4, 4, ...
5, 8, 9, 16, 5, 5, 5, 5, 5, 5, 5, ...
6, 9, 10, 17, 32, 6, 6, 6, 6, 6, 6, ...
7, 10, 16, 18, 33, 64, 7, 7, 7, 7, 7, ...
8, 13, 17, 19, 34, 65, 128, 8, 8, 8, 8, ...
9, 16, 24, 32, 35, 66, 129, 256, 9, 9, 9, ...
10, 17, 27, 33, 36, 67, 130, 257, 512, 10, 10, ...
MAPLE
A:= proc() local l, w, A; l, w, A:= proc() [] end, proc() [] end,
proc(n, k) option remember; local b; b:=
proc(x, y) option remember; `if`(x<0 or y<1, {},
{0, b(x, y-1)[], map(t-> t+l(k)[y], b(x-1, y))[]})
end;
while nops(w(k)) < n do forget(b);
l(k):= [l(k)[], (nops(l(k))+1)^k];
w(k):= sort([select(h-> h<l(k)[-1], b(k, nops(l(k))))[]])
od; w(k)[n]
end; A
end():
seq(seq(A(n, 1+d-n), n=1..d), d=1..14);
MATHEMATICA
b[n_, k_, i_, t_] := b[n, k, i, t] = n == 0 || i > 0 && t > 0 && (b[n, k, i - 1, t] || i^k <= n && b[n - i^k, k, i, t - 1]);
A[n_, k_] := A[n, k] = Module[{m}, For[m = 1 + If[n == 1, -1, A[n - 1, k]], !b[m, k, m^(1/k) // Floor, k], m++]; m];
Table[A[n, 1+d-n], {d, 1, 14}, {n, 1, d}] // Flatten (* Jean-François Alcover, Dec 03 2020, using Alois P. Heinz's code for columns *)
CROSSREFS
A(n+j,n) for j=0-3 give: A001477(n-1), A000027, A000079, A000051.
Cf. A336725.
Sequence in context: A362327 A350168 A262881 * A099173 A293377 A159880
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Aug 04 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)