|
%I #15 Oct 18 2023 09:08:40
%S 1,1,2,4,8,15,28,52,96,177,345,694,1386,2751,5431,10672,20885,40724,
%T 79153,153402,296528,571845,1129293,2264749,4527029,9021498,17926740,
%U 35527082,70230422,138504765,272545323,535184340,1048842743,2051669285,4006253136,7954830148
%N a(n) is the largest number in the n-th row of triangle A140997.
%C Also the largest number of the n-th row of A140994.
%H Juri-Stepan Gerasimov, <a href="/A140998/a140998.jpg">Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...</a>
%e The largest number of 1 is a(0) = 1.
%e The largest number of 1 1 is a(1) = 1.
%e The largest number of 1 2 1 is a(2) = 2.
%e The largest number of 1 4 2 1 is a(3) = 4.
%e The largest number of 1 8 4 2 1 is a(4) = 8.
%e The largest number of 1 15 9 4 2 1 is a(5) = 15.
%e The largest number of 1 28 19 9 4 2 1 is a(6) = 28.
%e The largest number of 1 52 40 19 9 4 2 1 is a(7) = 52.
%p 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:
%p 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
%t 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]];
%t a[n_] := Max[Table[T[n, k], {k, 0, n}]];
%t Table[a[n], {n, 0, 60}] (* _Jean-François Alcover_, Oct 18 2023, after _R. J. Mathar_ *)
%Y Cf. A007318, A140993, A140994, A140995, A140996, A140997, A140998, A141020, A141021.
%K nonn
%O 0,3
%A _Juri-Stepan Gerasimov_, Jul 11 2008
%E Partially edited by _N. J. A. Sloane_, Jul 18 2008
%E Simplified definition, corrected from a(12) on and extended by _R. J. Mathar_, Sep 19 2008
|
