A026299 Number of (s(0), s(1), ..., s(n)) such that every s(i) is a nonnegative integer, s(0) = 0, s(1) = 1, |s(i) - s(i-1)| <= 1 for i >= 2, |s(2) - s(1)| = 1, |s(3) - s(2)| = 1 if s(2) = 1. Also sum of numbers in row n+1 of the array T in A026268.

1, 3, 7, 19, 53, 149, 422, 1202, 3440, 9884, 28495, 82387, 238801, 693689, 2018981, 5886329, 17187891, 50257299, 147135189, 431245977, 1265264799, 3715761759, 10921722348, 32127865392, 94578844458, 278614855862, 821281118993, 2422356077357, 7148679142639

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

Cf. A026268.

Programs

Maple

A026268 := proc(nmax) local T,i,j; T := array(0..nmax,0..nmax) ; for i from 0 to nmax do T[i,0] := 1; od ; T[1,1] := 1 ; if nmax >= 2 then T[2,1] := 1 ; T[2,2] := 1 ; fi ; if nmax >= 3 then T[3,1] := 2 ; T[3,2] := 2 ; T[3,3] := 2 ; fi ; for i from 4 to nmax do T[i,1] := i-1 ; T[i,i] := T[i-1,i-2]+T[i-1,i-1] ; for j from 2 to i-1 do T[i,j] := T[i-1,j-2]+T[i-1,j-1]+T[i-1,j] ; od ; od ; RETURN(T) ; end: A026299 := proc(n) local T ; if n =0 then RETURN(1) ; else T := A026268(n+1) ; sum(T[n+1,i],i=0..n+1) ; fi ; end ; for n from 0 to 30 do printf("%d,",A026299(n)) ; od ; # R. J. Mathar, Oct 31 2006

Formula

Conjecture: (n+2)*a(n) +(-3*n-4)*a(n-1) +(-n+2)*a(n-2) +3*(n-4)*a(n-3)=0. - R. J. Mathar, Jun 23 2013

Extensions

Corrected and extended by R. J. Mathar, Oct 31 2006