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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A259976 Irregular triangle T(n, k) read by rows (n >= 0, 0 <= k <= A011848(n)): T(n, k) is the number of occurrences of the principal character in the restriction of xi_k to S_(n)^(2). 2
 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 0, 1, 3, 4, 6, 6, 3, 1, 0, 1, 3, 5, 11, 20, 24, 32, 34, 17, 1, 0, 1, 3, 6, 13, 32, 59, 106, 181, 261, 317, 332, 245, 89, 1, 0, 1, 3, 6, 14, 38, 85, 197, 426, 866, 1615, 2743, 4125, 5495, 6318, 6054, 4416, 1637 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS See Merris and Watkins (1983) for precise definition. LINKS Russell Merris and William Watkins, Tensors and graphs, SIAM J. Algebraic Discrete Methods 4 (1983), no. 4, 534-547. Andrey Zabolotskiy, a259976 (implementation in Rust). FORMULA From Andrey Zabolotskiy, Aug 28 2018: (Start) Sum_{ k=0..A011848(n) } T(n,k) * (n*(n-1)/2 - 2*k + 1) = A000088(n). T(n,k) = A005368(k) for n >= 2*k. (End) EXAMPLE The triangle begins: [0] 1 [1] 1 [2] 1 [3] 1,0, [4] 1,0,1,1, [5] 1,0,1,2,2,0, [6] 1,0,1,3,4,6,6,3, [7] 1,0,1,3,5,11,20,24,32,34,17 [8] 1,0,1,3,6,13,32,59,106,181,261,317,332,245,89 [9] 1,0,1,3,6,14,38,85,197,426,866,1615,2743,4125,5495,6318,6054,4416,1637 ... PROG (Sage) from sage.groups.perm_gps.permgroup_element import make_permgroup_element for p in range(8):     m = p*(p-1)//2     Sm = SymmetricGroup(m)     denom = factorial(p)     elements = []     for perm in SymmetricGroup(p):         t = perm.tuple()         eperm = []         for v2 in range(p):             for v1 in range(v2):                 w1, w2 = sorted([t[v1], t[v2]])                 eperm.append((w2-1)*(w2-2)//2+w1)         elements.append(make_permgroup_element(Sm, eperm))     for q in range(m//2+1):         char = SymmetricGroupRepresentation([m-q, q]).to_character()         numer = sum(char(e) for e in elements)         print((p, q), numer//denom) # Andrey Zabolotskiy, Aug 28 2018 CROSSREFS Cf. A005368, A000088, A011848. Length of row n is A039823(n-1). Sequence in context: A332902 A204423 A112170 * A113685 A049825 A287443 Adjacent sequences:  A259973 A259974 A259975 * A259977 A259978 A259979 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Jul 12 2015 EXTENSIONS Name edited, terms T(7, 9)-T(7, 10) and rows 0-2, 8, 9 added by Andrey Zabolotskiy, Sep 06 2018 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 May 31 13:01 EDT 2020. Contains 334748 sequences. (Running on oeis4.)