A205494 Conjectured row or column n=4 of array A205497.

1, 26, 334, 2951, 20641, 123216, 656683, 3217526, 14786816, 64657546, 271838823, 1107586989, 4399926007, 17122243560, 65514790830, 247212893755, 922136438698, 3406871213836, 12486569116765, 45459575562313, 164578100859837, 593025025473647, 2128399709975819, 7613495897772440

Offset

0,2

Comments

The denominator of the generating function for this sequence is a polynomial of degree 35. Terms corresponding to n=0,...,23 are shown above, with those for n=24,...,40 as follows: {27157723973468595, 96643368020414337, 343226612286408932, 1216901732483780905, 4308339945395597755, 15234940157670046379, 53818220864065451564, 189952299613455045068, 669953408386151161398, 2361449534293944339096, 8319329987059336296021, 29296032314800671782284, 103126374236214419873734, 362907786820798388773987, 1276761054260676178577043, 4490840947292979020061377, 15793032895427304036405557}.

See A205497 regarding association of this sequence with generating functions for the rows of the tabular form of A050446.

Links

Table of n, a(n) for n=0..23.

L. E. Jeffery, Unit-primitive matrices

Formula

G.f.: (1+4*x-31*x^2 - 67*x^3 + 348*x^4 + 418*x^5 - 1893*x^6 - 1084*x^7 + 4326*x^8 + 4295*x^9 - 7680*x^10 - 9172*x^11 + 9104*x^12 + 11627*x^13 - 5483*x^14 - 10773*x^15 + 1108*x^16 + 7255*x^17 + 315*x^18 - 3085*x^19 - 228*x^20 + 669*x^21 + 102*x^22 - 23*x^23 - 45*x^24 - 16*x^25 + 11*x^26 + 2*x^27 - x^28) / ((1-x)^5 * (1-x-x^2)^4 * (1-2*x-x^2+x^3)^3 * (1-2*x-3*x^2+x^3+x^4)^2 * (1-3*x-3*x^2+4*x^3+x^4-x^5)).

CONJECTURE 1. a(n) = M_{n,4} = M_{4,n}, where M = A205497.

CONJECTURE 2. Let w=2*cos(Pi/11). Then lim_{n->oo} a(n+1)/a(n) = w^4-3*w^2+1 = spectral radius of the 5 X 5 unit-primitive matrix (see [Jeffery]) A_{11,4} = [0,0,0,0,1; 0,0,0,1,1; 0,0,1,1,1; 0,1,1,1,1; 1,1,1,1,1].

Crossrefs

Cf. A205497, A050446, A050447.

Sequence in context: A010942 A022621 A085743 * A125438 A126919 A035708

Adjacent sequences: A205491 A205492 A205493 * A205495 A205496 A205497

Keyword

nonn

Author

L. Edson Jeffery, Jan 28 2012

Status

approved