A141018 a(n) is the largest number in the n-th row of triangle A140997.

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.

Links

Table of n, a(n) for n=0..35.

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

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 *)

Crossrefs

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

Sequence in context: A073769 A008937 A128805 * A049864 A239554 A268393

Adjacent sequences: A141015 A141016 A141017 * A141019 A141020 A141021

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jul 11 2008

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