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
Keywords
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 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.
Links
- Juri-Stepan Gerasimov, Stepan's triangles and Pascal's triangle are connected by the recurrence relation ...
Programs
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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
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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 *)
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
Comments