A141019 a(n) is the largest number in the n-th row of triangle A140996.

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

Author

Juri-Stepan Gerasimov, Jul 11 2008

Keywords

• nonn

Comments

Also the largest number in the n-th row of A140995.

Examples

			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.
		

Links

• Juri-Stepan Gerasimov, Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...

Crossrefs

Cf. A007318, A140993, A140994, A140995, A140996, A140997, A140998, A141020, A141021.

Programs

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 *)

Formula

a(n) = max_{k=0..n} A140996(n,k).

Extensions

Partially edited by N. J. A. Sloane, Jul 18 2008

Simplified definition and extended by R. J. Mathar, Sep 19 2008