cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A339798 Number of (undirected) Hamiltonian paths in the graph C_4 X C_n.

Original entry on oeis.org

4128, 45696, 287160, 2172480, 11866848, 76468352, 390714840, 2301083680, 11288784144, 62812654272, 299720429528, 1604776566400, 7505573487360, 39105991164160, 180179056818584, 920223907284960, 4191443432295472, 21088555826121280, 95195388883597464, 473503955161244480
Offset: 3

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Author

Seiichi Manyama, Dec 17 2020

Keywords

Crossrefs

Programs

  • Python
    # Using graphillion
    from graphillion import GraphSet
    def make_CnXCk(n, k):
        grids = []
        for i in range(1, k + 1):
            for j in range(1, n):
                grids.append((i + (j - 1) * k, i + j * k))
            grids.append((i + (n - 1) * k, i))
        for i in range(1, k * n, k):
            for j in range(1, k):
                grids.append((i + j - 1, i + j))
            grids.append((i + k - 1, i))
        return grids
    def A(start, goal, n, k):
        universe = make_CnXCk(n, k)
        GraphSet.set_universe(universe)
        paths = GraphSet.paths(start, goal, is_hamilton=True)
        return paths.len()
    def B(n, k):
        m = k * n
        s = 0
        for i in range(1, m):
            for j in range(i + 1, m + 1):
                s += A(i, j, n, k)
        return s
    def A339798(n):
        return B(n, 4)
    print([A339798(n) for n in range(3, 10)])

A358869 Number of (undirected) paths in the graph C_5 X C_n.

Original entry on oeis.org

6690, 324570, 10489660, 276182500, 6486444750, 141606011050, 2938679135800, 58759814756160, 1142125726154350, 21713533582158110, 405578743418707380, 7468021173224848600, 135906384557097211050, 2449354951706961634050, 43785800216111451354800, 777390470051273329332440, 13722022446524862502553730
Offset: 2

Views

Author

Seiichi Manyama, Dec 03 2022

Keywords

Crossrefs

Extensions

a(8)-a(18) from Andrew Howroyd, Jan 28 2023
a(2) prepended by Ed Wynn, Jul 07 2023

A358870 Number of (undirected) Hamiltonian paths in the graph C_6 X C_n.

Original entry on oeis.org

3264, 73368, 2172480, 29861820, 560028096, 6632769528, 103075391424, 1156940480232, 16166871906480, 176333810290572, 2300510733948576, 24611138715163572, 306092489935215648, 3227108582232289260, 38755349620705085952, 403867959699992233836, 4722889110592680685152, 48750193590184268147100
Offset: 2

Views

Author

Seiichi Manyama, Dec 04 2022

Keywords

Crossrefs

Extensions

More terms from Ed Wynn, Jul 07 2023
Showing 1-3 of 3 results.