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 A024996 Triangular array, read by rows: second differences in n,n direction of trinomial array A027907. 18
 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 5, 6, 8, 6, 5, 2, 1, 1, 3, 8, 13, 19, 20, 19, 13, 8, 3, 1, 1, 4, 12, 24, 40, 52, 58, 52, 40, 24, 12, 4, 1, 1, 5, 17, 40, 76, 116, 150, 162, 150, 116, 76, 40, 17, 5, 1, 1, 6, 23, 62, 133, 232, 342, 428, 462, 428, 342, 232, 133, 62, 23, 6 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS For n>2, T(n,k) = number of integer strings s(0),...,s(n) such that s(n)=n-k, s(0)=0, |s(i)-s(i-1)|=1 for i=1,2 and <=1 for i >= 3. LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened FORMULA T(n, k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), starting with [1], [1, 0, 1], [1, 0, 2, 0, 1]. G.f.: (1-yz)^2 / [1-z(1+y+y^2)]. - Ralf Stephan, Jan 09 2005 EXAMPLE .............1 ..........1..0..1 .......1..0..2..0..1 .....1.1..3..2..3..1..1 ...1.2.5..6..8..6..5..2.1 .1.3.8.13.19.20.19.13.8.3.1 MAPLE A024996 := proc(n, k)     option remember;     if n < 0 or k < 0 or k > 2*n then         0 ;     elif n <= 2 then         if k = 2*n or k = 0 then             1;         elif k = 2*n-1 or k = 1 then             0;         elif k =2 then             2;         end if;     else         procname(n-1, k-1)+procname(n-1, k-2)+procname(n-1, k) ;     end if; end proc: # R. J. Mathar, Jun 23 2013 MATHEMATICA CoefficientList[CoefficientList[Series[(1 - y*x)^2/(1 - x*(1 + y + y^2)), {x, 0, 10}, {y, 0, 10}], x], y] // Flatten (* G. C. Greubel, May 22 2017 *) PROG (PARI) T(n, k)=if(n<0||k<0||k>2*n, 0, if(n==0, 1, if(n==1, [1, 0, 1][k+1], if(n==2, [1, 0, 2, 0, 1][k+1], T(n-1, k-2)+T(n-1, k-1)+T(n-1, k))))) CROSSREFS First differences in n, n direction of array A025177. Central column is essentially A024997, other columns are A024998, A026069, A026070, A026071. Row sums are in A025579. Cf. A024072. Sequence in context: A029394 A035467 A254045 * A187596 A263863 A134655 Adjacent sequences:  A024993 A024994 A024995 * A024997 A024998 A024999 KEYWORD nonn,tabf,easy AUTHOR EXTENSIONS Edited by Ralf Stephan, Jan 09 2004 Offset corrected by R. J. Mathar, Jun 23 2013 STATUS approved

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Last modified February 21 02:57 EST 2019. Contains 320364 sequences. (Running on oeis4.)