2,2

Seiichi Manyama, Table of n, a(n) for n = 2..1000

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

Index entries for linear recurrences with constant coefficients, signature (3,21,44,-5,-47,-26,83,-81,39,-10,1)

a(n) = 3*a(n-1) + 21*a(n-2) + 44*a(n-3) - 5*a(n-4) - 47*a(n-5) - 26*a(n-6) + 83*a(n-7) - 81*a(n-8) + 39*a(n-9) - 10*a(n-10) + a(n-11) for n > 12.

G.f.: x^2*(1 + 10*x + 20*x^2 - 8*x^3 - 43*x^4 + 9*x^5 + 34*x^6 - 42*x^7 + 24*x^8 - 7*x^9 + x^10) / (1 - 3*x - 21*x^2 - 44*x^3 + 5*x^4 + 47*x^5 + 26*x^6 - 83*x^7 + 81*x^8 - 39*x^9 + 10*x^10 - x^11). - Vaclav Kotesovec, Dec 23 2020

CoefficientList[Series[x^2(1+10x+20x^2-8x^3-43x^4+9x^5+34x^6-42x^7+24x^8-7x^9+x^10)/(1-3x-21x^2-44x^3+5x^4+47x^5+26x^6-83x^7+81x^8-39x^9+10x^10-x^11), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 21, 44, -5, -47, -26, 83, -81, 39, -10, 1}, {1, 13, 80, 549, 3851, 26499, 183521, 1269684, 8782833, 60764640, 420375910}, 30] (* Harvey P. Dale, Mar 30 2023 *)

(PARI) N=40; a=vector(N); a[2]=1; a[3]=13; a[4]=80; a[5]=549; a[6]=3851; a[7]=26499; a[8]=183521; a[9]=1269684; a[10]=8782833; a[11]=60764640; a[12]=420375910; for(n=13, N, a[n]=3*a[n-1]+21*a[n-2]+44*a[n-3]-5*a[n-4]-47*a[n-5]-26*a[n-6]+83*a[n-7]-81*a[n-8]+39*a[n-9]-10*a[n-10]+a[n-11]); a[2..N]

(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 A339851(n):

return A339849(4, n)

print([A339851(n) for n in range(2, 21)])

Row 4 of A339849.

Cf. A339201.

Sequence in context: A071614 A045552 A264381 * A297678 A189451 A133718

Adjacent sequences: A339848 A339849 A339850 * A339852 A339853 A339854

Seiichi Manyama, Dec 19 2020

approved