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A205495 Convolution related to array A205497 and to generating functions for the rows of the array form of A050446. 0
1, 46, 937, 12331, 123216, 1019051, 7349140, 47816612, 287357460, 1622135139, 8709442871, 44899559053, 223883501478, 1086005140508, 5148332487873, 23940669359515, 109535136537197, 494307574790201, 2204762394907238, 9736270202183689, 42629974672006973 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The denominator of the generating function for this sequence is a polynomial of degree 56. Terms corresponding to n=0,...,20 are shown above, with those for n=21,...,60 as follows: {185291835954412064, 800317930217099771, 3438057983187970745, 14700487950597800766, 62602970565114993286, 265668524077091893747, 1124012759249695584332, 4743119424920236606646, 19969635838069446154607, 83911303727287364502524, 351988383031210413076295, 1474320303050934448138586, 6167313972271997160616487, 25770018446823167711177256, 107575128852482376189099657, 448686576996876913475900985, 1870064613139417627428681546, 7789228056784680467763728356, 32425967246106296890368810943, 134922331498272588364476180150, 561170234171421424687450762218, 2333185213162875626980569334586, 9697691681023767935816546925810, 40296761019115897693378020750304, 167405678599573178754554735425500, 695315826495982432201817860350384, 2887471697263577884599209836720724, 11989119731801937435908186367502418, 49773672878387017240820277186133933, 206615368239595050328432096365772786, 857596063782668973911429246019645248, 3559311146445642266628947699835442405, 14771247245703845390492597474797181501, 61297218039066894581942073485999795498, 254355134654745436101804689307395799176, 1055406241452059982356995468881303135245, 4379061349078358899285795579448995148357, 18168834136106060681393826933553149199771, 75380646388163385087709907289615387511431, 312738422596514964765543905180978445030357}.

LINKS

Table of n, a(n) for n=0..20.

L. E. Jeffery, Unit-primitive matrices

FORMULA

G.f.: F(x) = (1 + 12*x - 112*x^2 - 343*x^3 + 3560*x^4 + 765*x^5 - 40847*x^6 + 10585*x^7 + 310877*x^8 - 193248*x^9 - 1419395*x^10 + 785781*x^11 + 5312667*x^12 - 2323912*x^13 - 15628824*x^14 + 5966469*x^15 + 33782788*x^16 - 10059915*x^17 - 55526776*x^18 + 8186536*x^19 + 73510769*x^20 + 2472617*x^21 - 80001340*x^22 - 15202136*x^23 + 70051834*x^24 + 21752017*x^25 - 47710282*x^26 - 20490103*x^27 + 24620158*x^28 + 14731526*x^29 - 9477868*x^30 - 8317984*x^31 + 2706852*x^32 + 3624852*x^33 - 575397*x^34 - 1176133*x^35 + 88180*x^36 + 269838*x^37 - 5571*x^38 - 39836*x^39 - 2463*x^40 + 2831*x^41 + 1104*x^42 + 107*x^43 - 221*x^44 - 36*x^45 + 23*x^46 + 2*x^47 - x^48) / ((1-x)^6 * (1-x-x^2)^5 * (1-2*x-x^2+x^3)^4 * (1-2*x-3*x^2+x^3+x^4)^3 * (1-3*x-3*x^2+4*x^3+x^4-x^5)^2 * (1-3*x-6*x^2+4*x^3+5*x^4-x^5-x^6)).

CONJECTURE 1. a(n) = M_{n,5} = M_{5,n}, where M = A205497.

CONJECTURE 2. Let w=2*cos(Pi/13). Then lim_{n -> infinity) a(n+1)/a(n) = w^5-4*w^3+3*w = spectral radius of the 6 X 6 unit-primitive matrix (see [Jeffery]) A_{13,5} = [0,0,0,0,0,1; 0,0,0,0,1,1; 0,0,0,1,1,1; 0,0,1,1,1,1; 0,1,1,1,1,1; 1,1,1,1,1,1].

CROSSREFS

Cf. A205497, A050446, A050447.

Sequence in context: A156842 A078427 A002138 * A281655 A280280 A010962

Adjacent sequences: A205492 A205493 A205494 * A205496 A205497 A205498

KEYWORD

nonn

AUTHOR

L. Edson Jeffery, Jan 28 2012

STATUS

approved

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Last modified November 28 05:56 EST 2022. Contains 358407 sequences. (Running on oeis4.)