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%I #15 Jan 28 2024 14:33:59
%S 1,1,2,4,8,16,31,60,116,224,432,833,1606,3096,5968,11504,22175,42744,
%T 84752,169880,340013,679604,1356641,2704954,5387340,10718620,21304973,
%U 42308331,83945336,166423276,329683867,652627294,1291020297,2552209710,5042305104
%N a(n) is the largest number in the n-th row of triangle A140996.
%C Also the largest number in the n-th row of A140995.
%H Juri-Stepan Gerasimov, <a href="/A140998/a140998.jpg">Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...</a>
%F a(n) = max_{k=0..n} A140996(n,k).
%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 16 8 4 2 1 is a(5) = 16.
%e The largest number of 1 31 17 8 4 2 1 is a(6) = 31.
%p 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:
%p 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
%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, 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]];
%t a[n_] := Table[T[n, k], {k, 0, n}] // Max;
%t Table[a[n], {n, 0, 34}] (* _Jean-François Alcover_, Jan 28 2024, 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 and extended by _R. J. Mathar_, Sep 19 2008
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