cp's OEIS Frontend

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.

%I A026299 #12 Jan 01 2024 23:49:16
%S A026299 1,3,7,19,53,149,422,1202,3440,9884,28495,82387,238801,693689,2018981,
%T A026299 5886329,17187891,50257299,147135189,431245977,1265264799,3715761759,
%U A026299 10921722348,32127865392,94578844458,278614855862,821281118993,2422356077357,7148679142639
%N 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.
%F A026299 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
%p A026299 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
%Y A026299 Cf. A026268.
%K A026299 nonn
%O A026299 0,2
%A A026299 _Clark Kimberling_
%E A026299 Corrected and extended by _R. J. Mathar_, Oct 31 2006