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 A195522 T(n,k) = Number of lower triangles of an n X n -k..k array with all row and column sums zero. 12
 1, 1, 1, 1, 1, 3, 1, 1, 5, 15, 1, 1, 7, 65, 199, 1, 1, 9, 175, 3753, 6247, 1, 1, 11, 369, 27267, 860017, 505623, 1, 1, 13, 671, 121367, 23663523, 839301197, 105997283, 1, 1, 15, 1105, 401565, 286168923, 122092290831, 3535646416019, 58923059879, 1, 1, 17 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS Table starts ....1......1........1.........1..........1...........1...........1.......1....1 ....1......1........1.........1..........1...........1...........1.......1....1 ....3......5........7.........9.........11..........13..........15......17...19 ...15.....65......175.......369........671........1105........1695....2465.3439 ..199...3753....27267....121367.....401565.....1089411.....2563933.5423365 .6247.860017.23663523.286168923.2106810049.11131321791.46387885537 LINKS R. H. Hardin, Table of n, a(n) for n = 1..75 FORMULA Empirical for rows: T(2,k) = 1 T(3,k) = 2*k + 1 T(4,k) = 4*k^3 + 6*k^2 + 4*k + 1 T(5,k) = (643/45)*k^6 + (643/15)*k^5 + (2165/36)*k^4 + (293/6)*k^3 + (4423/180)*k^2 + (73/10)*k + 1 T(6,k) = (7389349/90720)*k^10 + (7389349/18144)*k^9 + (836251/864)*k^8 + (4318165/3024)*k^7 + (6254923/4320)*k^6 + (4563293/4320)*k^5 + (10247161/18144)*k^4 + (249983/1134)*k^3 + (21959/360)*k^2 + (3469/315)*k + 1 EXAMPLE Some solutions for n=5 k=6 ..0..........0..........0..........0..........0..........0..........0 ..0.0.......-2.2........6-6.......-1.1........5-5.......-4.4.......-4.4 .-1.3-2.....-6.0.6.....-6.6.0.....-1.5-4.....-6.4.2......3-6.3.....-4.1.3 ..6-3-2-1....4-4-4.4....5.3-5-3....0-5.3.2....0.4-3-1...-5.5.1-1....5-2-4.1 .-5.0.4.1.0..4.2-2-4.0.-5-3.5.3.0..2-1.1-2.0..1-3.1.1.0..6-3-4.1.0..3-3.1-1.0 CROSSREFS Row 4 is A005917(n+1). Sequence in context: A341470 A293796 A195892 * A273169 A273167 A324284 Adjacent sequences: A195519 A195520 A195521 * A195523 A195524 A195525 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Sep 20 2011 STATUS approved

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Last modified June 2 11:44 EDT 2023. Contains 363097 sequences. (Running on oeis4.)