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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A339852 Number of Hamiltonian circuits within parallelograms of size 5 X n on the triangular lattice. 2
1, 44, 549, 7104, 104100, 1475286, 20842802, 295671198, 4190083085, 59374628434, 841470846944, 11925007688342, 168996943899738, 2394974040514288, 33940795571394262, 480998063196253650, 6816550836218124869, 96601974078400509612, 1369012239935377295854, 19401203058253673198258 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 2..500

M. Peto, Studies of protein designability using reduced models, Thesis, 2007.

Index entries for linear recurrences with constant coefficients, signature (8,62,384,160,-1628,-11310,9700,-16019,102564, -98380,263340, -429661,174728,-361330,147404,284641,24764,182412,-156248, -138559,14756,14496,-3660,-2640,328,80,-8)

FORMULA

a(2)..a(31) = [1, 44, 549, 7104, 104100, 1475286, 20842802, 295671198, 4190083085, 59374628434, 841470846944, 11925007688342, 168996943899738, 2394974040514288, 33940795571394262, 480998063196253650, 6816550836218124869, 96601974078400509612, 1369012239935377295854, 19401203058253673198258, 274947636268050621400764, 3896469848341602644039976, 55219522831075639350876744, 782553393257523404353337072, 11090096073215866151573834374, 157165289898796544200350430624, 2227296155585971455156172389428, 31564527815820044279227403214372, 447322379530320420841684880901414, 6339309505792160540792742125116082] and

a(n) = 8*a(n-1) + 62*a(n-2) + 384*a(n-3) - 160*a(n-4) - 1628*a(n-5) - 11310*a(n-6) + 9700*a(n-7) - 16019*a(n-8) + 102564*a(n-9) - 98380*a(n-10) + 263340*a(n-11) - 429661*a(n-12) + 174728*a(n-13) - 361330*a(n-14) + 147404*a(n-15) + 284641*a(n-16) + 24764*a(n-17) + 182412*a(n-18) - 156248*a(n-19) - 138559*a(n-20) + 14756*a(n-21) + 14496*a(n-22) - 3660*a(n-23) - 2640*a(n-24) + 328*a(n-25) + 80*a(n-26) - 8*a(n-27) for n > 31.

PROG

(Python)

# Using graphillion

from graphillion import GraphSet

def make_T_nk(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))

            if i < k:

                grids.append((i + (j - 1) * k, i + j * k + 1))

    for i in range(1, k * n, k):

        for j in range(1, k):

            grids.append((i + j - 1, i + j))

    return grids

def A339849(n, k):

    universe = make_T_nk(n, k)

    GraphSet.set_universe(universe)

    cycles = GraphSet.cycles(is_hamilton=True)

    return cycles.len()

def A339852(n):

    return A339849(5, n)

print([A339852(n) for n in range(2, 21)])

CROSSREFS

Row 5 of A339849.

Cf. A339202.

Sequence in context: A222514 A282645 A283541 * A202075 A297680 A264680

Adjacent sequences:  A339849 A339850 A339851 * A339853 A339854 A339855

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 19 2020

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 17:37 EDT 2021. Contains 348215 sequences. (Running on oeis4.)