This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A071947 Triangle read by rows of numbers of paths in a lattice satisfying certain conditions. 3
 1, 1, 0, 1, 1, 1, 1, 2, 3, 1, 1, 3, 6, 6, 3, 1, 4, 10, 15, 15, 6, 1, 5, 15, 29, 40, 36, 15, 1, 6, 21, 49, 84, 105, 91, 36, 1, 7, 28, 76, 154, 238, 280, 232, 91, 1, 8, 36, 111, 258, 468, 672, 750, 603, 232, 1, 9, 45, 155, 405, 837, 1398, 1890, 2025, 1585, 603, 1, 10, 55, 209, 605 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad J. Math., 49 (1997), 301-320. FORMULA G.f.: t*(1+t*z-q)/[(1+t*z)*(2*t^2*z +t*z - 1 + q)], where q = sqrt(1 -2*t*z -3*t^2*z^2). Sum_{k, 0<=k<=n} T(n,k)*2^(n-k) = A112657(n). - Philippe Deléham, Apr 01 2007 T(n,k) = A027907(n,k) - A027907(n,k-1). T(n,n) = A005043(n). # Peter Luschny, Oct 01 2014 EXAMPLE Triangle begins   1;   1,  0;   1,  1,  1;   1,  2,  3,  1;   1,  3,  6,  6,  3;   1,  4, 10, 15, 15,  6; MAPLE A071947_row := proc(n) local G, k; G := expand((1+x+x^2)^n): seq(coeff(G, x, k) - coeff(G, x, k-1), k=0..n) end: seq(print(A071947_row(n)), n=0..11); # Peter Luschny, Oct 01 2014 MATHEMATICA A027907[n_, k_] := Sum[Binomial[n, j]*Binomial[j, k - j], {j, 0, n}]; A005043[n_] := Sum[(-1)^k*Binomial[n, k]*Binomial[k, Floor[k/2]], {k, 0, n}]; T[n_, k_] := A027907[n, k] - A027907[n, k - 1]; T[n_, n_] := A005043[n]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Mar 02 2017 *) CROSSREFS Row sums give A002426 (central trinomial coefficients). Reversal of A089942. Cf. A027907. Sequence in context: A265848 A139438 A135392 * A139343 A059247 A244665 Adjacent sequences:  A071944 A071945 A071946 * A071948 A071949 A071950 KEYWORD nonn,easy,tabl AUTHOR N. J. A. Sloane, Jun 15 2002 EXTENSIONS Edited by Emeric Deutsch, Mar 04 2004 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 21 11:05 EDT 2019. Contains 328294 sequences. (Running on oeis4.)