This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A241477 Triangle read by rows, number of orbitals classified with respect to the first zero crossing, n>=1, 1<=k<=n. 13
 1, 0, 2, 2, 2, 2, 0, 4, 0, 2, 6, 12, 4, 2, 6, 0, 12, 0, 4, 0, 4, 20, 60, 12, 12, 12, 4, 20, 0, 40, 0, 12, 0, 8, 0, 10, 70, 280, 40, 60, 36, 24, 40, 10, 70, 0, 140, 0, 40, 0, 24, 0, 20, 0, 28, 252, 1260, 140, 280, 120, 120, 120, 60, 140, 28, 252, 0, 504, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For the combinatorial definitions see A232500. An orbital w over n sectors has its first zero crossing at k if k is the smallest j such that the partial sum(1<=i<=j, w(i))) = 0, where w(i) are the jumps of the orbital represented by -1, 0, 1. LINKS FORMULA If n is even and k is odd then T(n, k) = 0 else if k = 1 then T(n, 1) = A056040(n-1) else T(n, k) = 2*A057977(k-2)*A056040(n-k). T(n, n) = A241543(n). T(n+1, 1) = A126869(n). T(2*n, 2*n) = |A002420(n)|. T(2*n+1, 1) = A000984(n). T(2*n+1, n+1) = A241530(n). T(2*n+2, 2) = A028329(n). T(4*n, 2*n) = |A010370(n)|. T(4*n, 4*n) = |A024491(n)|. T(4*n+1, 1) = A001448(n). T(4*n+1, 2*n+1) = A002894(n). EXAMPLE [1], [ 1] [2], [ 0,  2] [3], [ 2,  2,  2] [4], [ 0,  4,  0,  2] [5], [ 6, 12,  4,  2,  6] [6], [ 0, 12,  0,  4,  0, 4] [7], [20, 60, 12, 12, 12, 4, 20] MAPLE A241477 := proc(n, k)   if n = 0 then 1 elif k = 0 then 0 elif irem(n, 2) = 0 and irem(k, 2) = 1 then 0 elif k = 1 then (n-1)!/iquo(n-1, 2)!^2 else 2*(n-k)!*(k-2)!/iquo(k, 2)/(iquo(k-2, 2)!*iquo(n-k, 2)!)^2   fi end: for n from 1 to 9 do seq(A241477(n, k), k=1..n) od; MATHEMATICA T[n_, k_] := Which[n == 0, 1, k == 0, 0, Mod[n, 2] == 0 && Mod[k, 2] == 1,  0, k == 1, (n-1)!/Quotient[n-1, 2]!^2, True, 2*(n-k)!*(k-2)!/Quotient[k, 2]/(Quotient[k-2, 2]!*Quotient[n-k, 2]!)^2]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 20 2018, from Maple *) PROG (Sage) def A241477_row(n):     if n == 0: return [1]     Z = [0]*n; T = [0] if is_odd(n) else []     for i in (1..n//2): T.append(-1); T.append(1)     for p in Permutations(T):         i = 0; s = p[0]         while s <> 0: i += 1; s += p[i];         Z[i] += 1     return Z for n in (1..9): A241477_row(n) CROSSREFS Row sums: A056040. Cf. A232500. Sequence in context: A214666 A320471 A127444 * A268243 A159782 A268242 Adjacent sequences:  A241474 A241475 A241476 * A241478 A241479 A241480 KEYWORD nonn,tabl AUTHOR Peter Luschny, Apr 23 2014 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 June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)