# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a064861 Showing 1-1 of 1 %I A064861 #42 Mar 19 2022 13:45:38 %S A064861 1,1,2,1,3,2,1,5,8,4,1,6,13,12,4,1,8,25,38,28,8,1,9,33,63,66,36,8,1, %T A064861 11,51,129,192,168,80,16,1,12,62,180,321,360,248,96,16,1,14,86,304, %U A064861 681,1002,968,592,208,32,1,15,100,390,985,1683,1970,1560,800,240,32,1,17 %N A064861 Triangle of Sulanke numbers: T(n,k) = T(n,k-1) + a(n-1,k) for n+k even and a(n,k) = a(n,k-1) + 2*a(n-1,k) for n+k odd. %C A064861 When A064861 is regarded as a triangle read by rows, this is [1,0,-1,0,0,0,0,0,0,...] DELTA [2,-1,-1,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Dec 14 2008 %H A064861 Reinhard Zumkeller, Rows n = 0..125 of table, flattened %H A064861 Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019. %H A064861 Milan Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550 [math.CO], 2013. - From _N. J. A. Sloane_, Feb 13 2013 %H A064861 Milan Janjic and B. Petkovic, A Counting Function Generalizing Binomial Coefficients and Some Other Classes of Integers, J. Int. Seq. 17 (2014) # 14.3.5. %H A064861 C. de Jesús Pita Ruiz Velasco, Convolution and Sulanke Numbers, JIS 13 (2010) 10.1.8. %H A064861 R. A. Sulanke, Problem 10894, Amer. Math. Monthly 108, (2001), p. 770. %F A064861 G.f.: Sum_{m>=0} Sum_{n>=0} a_{m, n}*t^m*s^n = A(t,s) = (1+2*t+s)/(1-2*t^2-s^2-3*s*t). %e A064861 Table begins: %e A064861 1, 1, 1, 1, 1, 1, 1, 1, ... %e A064861 2, 3, 5, 6, 8, 9, 11, ... %e A064861 2, 8, 13, 25, 33, 51, ... %e A064861 4, 12, 38, 63, 129, ... %e A064861 4, 28, 66, 192, ... %p A064861 A064861 := proc(n,k) option remember; if n = 1 then 1; elif k = 0 then 0; else procname(n,k-1)+(3/2-1/2*(-1)^(n+k))*procname(n-1,k); fi; end; %p A064861 seq(seq(A064861(i,j-i),i=1..j-1),j=1..19); %t A064861 max = 12; se = Series[(1 + 2*x + y*x)/(1 - 2*x^2 - y^2*x^2 - 3*y*x^2), {x, 0, max}, {y, 0, max}]; cc = CoefficientList[se, {x, y}]; Flatten[ Table[ cc[[n, k]], {n, 1, max}, {k, n, 1, -1}]] (* _Jean-François Alcover_, Oct 21 2011, after g.f. *) %o A064861 (PARI) a(n,m)=if(n<0 || m<0,0,polcoeff(polcoeff((1+2*x+y*x)/(1-2*x^2-y^2*x^2-3*y*x^2)+O(x^(n+m+1)),n+m),m)) %o A064861 (Haskell) %o A064861 a064861 n k = a064861_tabl !! n !! k %o A064861 a064861_row n = a064861_tabl !! n %o A064861 a064861_tabl = map fst $ iterate f ([1], 2) where %o A064861 f (xs, z) = (zipWith (+) ([0] ++ map (* z) xs) (xs ++ [0]), 3 - z) %o A064861 -- _Reinhard Zumkeller_, May 01 2014 %Y A064861 Cf. central Delannoy numbers a(n,n) = A001850(n), Delannoy numbers (same main diagonal): a(n,n) = A008288(n,n), a(n-1,n)=A002003(n), a(n,n+1)=A002002(n), a(n,1)=A058582(n), apparently a(n,n+2)=A050151(n). %K A064861 nonn,tabl,nice %O A064861 0,3 %A A064861 Barbara Haas Margolius (b.margolius(AT)csuohio.edu), Oct 10 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE