A309226 Index of n-th low point in A008348 (see Comments for definition).
0, 3, 8, 21, 56, 145, 366, 945, 2506, 6633, 17776, 48521, 133106, 369019, 1028404, 2880287, 8100948, 22877145, 64823568, 184274931, 525282740, 1501215193, 4299836186, 12340952049, 35486796312, 102220582465, 294917666854, 852123981581, 2465458792768
Offset: 0
Programs
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Maple
blocks := proc(a,S) local b,c,d,M,L,n; # Given a list a, whose leading term has index S, return [b,c,d], where b lists the indices of the low points in a, c lists the values of a at the low points, and d lists the length of runs between the low points. b:=[]; c:=[]; d:=[]; L:=1; # is a[1] a low point? n:=1; if( (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi; for n from 2 to nops(a)-2 do # is a[n] a low point? if( (a[n-1]>a[n]) and (a[n+1]>a[n]) and (a[n+2]>a[n+1]) ) then b:=[op(b),n+S-1]; c:=[op(c),a[n]]; d:=[op(d), n-L]; L:=n; fi; od; [b,c,d]; end; # Let a := [0, 2, 5, 0, 7, 18, 5, 22, 3, 26, 55, 24, ...]; be a list of the first terms in A008348 blocks(a,0)[1]; # the present sequence blocks(a,0)[2]; # A324782 blocks(a,0)[3]; # A324783
Formula
a(n) = A135025(n-1)-1.
Extensions
a(17)-a(28) from Giovanni Resta, Oct 02 2019
Modified definition to make offset 0. - N. J. A. Sloane, Oct 02 2019
Comments