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A141019
a(n) is the largest number in the n-th row of triangle A140996.
1
1, 1, 2, 4, 8, 16, 31, 60, 116, 224, 432, 833, 1606, 3096, 5968, 11504, 22175, 42744, 84752, 169880, 340013, 679604, 1356641, 2704954, 5387340, 10718620, 21304973, 42308331, 83945336, 166423276, 329683867, 652627294, 1291020297, 2552209710, 5042305104
OFFSET
0,3
COMMENTS
Also the largest number in the n-th row of A140995.
FORMULA
a(n) = max_{k=0..n} A140996(n,k).
EXAMPLE
The largest number of 1 is a(0) = 1.
The largest number of 1 1 is a(1) = 1.
The largest number of 1 2 1 is a(2) = 2.
The largest number of 1 4 2 1 is a(3) = 4.
The largest number of 1 8 4 2 1 is a(4) = 8.
The largest number of 1 16 8 4 2 1 is a(5) = 16.
The largest number of 1 31 17 8 4 2 1 is a(6) = 31.
MAPLE
A140996 := proc(n, k) option remember ; if k<0 or k>n then 0 ; elif k=0 or k=n then 1 ; elif k=n-1 then 2 ; elif k=n-2 then 4 ; elif k=n-3 then 8 ; else procname(n-1, k)+procname(n-2, k) +procname(n-3, k)+procname(n-4, k)+procname(n-4, k-1) ; fi; end:
A141019 := proc(n) max(seq(A140996(n, k), k=0..n)) ; end: for n from 0 to 50 do printf("%d, ", A141019(n)) ; od: # R. J. Mathar, Sep 19 2008
MATHEMATICA
T[n_, k_] := T[n, k] = Which[k < 0 || k > n, 0, k == 0 || k == n, 1, k == n - 1, 2, k == n-2, 4, k == n-3, 8, True, T[n-1, k] + T[n-2, k] + T[n-3, k] + T[n-4, k] + T[n-4, k-1]];
a[n_] := Table[T[n, k], {k, 0, n}] // Max;
Table[a[n], {n, 0, 34}] (* Jean-François Alcover, Jan 28 2024, after R. J. Mathar *)
KEYWORD
nonn
AUTHOR
EXTENSIONS
Partially edited by N. J. A. Sloane, Jul 18 2008
Simplified definition and extended by R. J. Mathar, Sep 19 2008
STATUS
approved