login
A141018
a(n) is the largest number in the n-th row of triangle A140997.
4
1, 1, 2, 4, 8, 15, 28, 52, 96, 177, 345, 694, 1386, 2751, 5431, 10672, 20885, 40724, 79153, 153402, 296528, 571845, 1129293, 2264749, 4527029, 9021498, 17926740, 35527082, 70230422, 138504765, 272545323, 535184340, 1048842743, 2051669285, 4006253136, 7954830148
OFFSET
0,3
COMMENTS
Also the largest number of the n-th row of A140994.
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 15 9 4 2 1 is a(5) = 15.
The largest number of 1 28 19 9 4 2 1 is a(6) = 28.
The largest number of 1 52 40 19 9 4 2 1 is a(7) = 52.
MAPLE
A140997 := 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 ; else procname(n-1, k)+procname(n-2, k)+procname(n-3, k)+procname(n-3, k-1) ; fi; end:
A141018 := proc(n) max(seq(A140997(n, k), k=0..n)) ; end: for n from 0 to 60 do printf("%d, ", A141018(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, True, T[n-1, k]+T[n-2, k]+T[n-3, k]+T[n-3, k-1]];
a[n_] := Max[Table[T[n, k], {k, 0, n}]];
Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Oct 18 2023, after R. J. Mathar *)
KEYWORD
nonn
AUTHOR
EXTENSIONS
Partially edited by N. J. A. Sloane, Jul 18 2008
Simplified definition, corrected from a(12) on and extended by R. J. Mathar, Sep 19 2008
STATUS
approved