The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A118343 Triangle, read by rows, where diagonals are successive self-convolutions of A108447. 3
 1, 1, 0, 1, 1, 0, 1, 2, 4, 0, 1, 3, 9, 20, 0, 1, 4, 15, 48, 113, 0, 1, 5, 22, 85, 282, 688, 0, 1, 6, 30, 132, 519, 1762, 4404, 0, 1, 7, 39, 190, 837, 3330, 11488, 29219, 0, 1, 8, 49, 260, 1250, 5516, 22135, 77270, 199140, 0, 1, 9, 60, 343, 1773, 8461, 37404, 151089 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS A108447 equals the central terms of pendular triangle A118340 and the diagonals of this triangle form the semi-diagonals of the triangle A118340. Row sums equal A054727, the number of forests of rooted trees with n nodes on a circle without crossing edges. LINKS FORMULA Since g.f. G=G(x) of A108447 satisfies: G = 1 - x*G + x*G^2 + x*G^3 then T(n,k) = T(n-1,k) - T(n-1,k-1) + T(n,k-1) + T(n+1,k-1). Also, a recurrence involving antidiagonals is: T(n,k) = T(n-1,k) + Sum_{j=1..k} [2*T(n-1+j,k-j) - T(n-2+j,k-j)] for n>k>=0. EXAMPLE Show: T(n,k) = T(n-1,k) - T(n-1,k-1) + T(n,k-1) + T(n+1,k-1) at n=8,k=4: T(8,4) = T(7,4) - T(7,3) + T(8,3) + T(9,3) or 837 = 519 - 132 + 190 + 260. Triangle begins: 1; 1, 0; 1, 1, 0; 1, 2, 4, 0; 1, 3, 9, 20, 0; 1, 4, 15, 48, 113, 0; 1, 5, 22, 85, 282, 688, 0; 1, 6, 30, 132, 519, 1762, 4404, 0; 1, 7, 39, 190, 837, 3330, 11488, 29219, 0; 1, 8, 49, 260, 1250, 5516, 22135, 77270, 199140, 0; 1, 9, 60, 343, 1773, 8461, 37404, 151089, 532239, 1385904, 0; ... PROG (PARI) {T(n, k)=polcoeff((serreverse(x*(1-x+sqrt((1-x)*(1-5*x)+x*O(x^k)))/2/(1-x))/x)^(n-k), k)} CROSSREFS Cf. A108447, A054727 (row sums), A118340. Sequence in context: A258761 A256245 A173004 * A309148 A226031 A308460 Adjacent sequences:  A118340 A118341 A118342 * A118344 A118345 A118346 KEYWORD nonn,tabl AUTHOR Paul D. Hanna, Apr 26 2006 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 December 2 06:44 EST 2020. Contains 338868 sequences. (Running on oeis4.)