A120714 -id:A120714 - cp's OEIS frontend

A120715 Sequence produced by 14 X 14 Markov chain based on 14-vertex graph formed from direct product of two copies of the graph used in A120714.

0, 27, 838, 4025, 29742, 161630, 962784, 5335471, 30120946, 166834881, 926998480, 5122817760, 28316610392, 156260679433, 862162027134, 4754345230927, 26214240435218, 144511100239056, 796592187757696

Offset: 0

Roger L. Bagula, Aug 12 2006, corrected Jul 14 2007

Characteristic polynomial: -17 - 96*x + 65*x^2 + 1528*x^3 + 3840*x^4 + 2996*x^5 - 1566*x^6 - 3312*x^7 - 702*x^8 + 880*x^9 + 372*x^10 - 52*x^11 - 37*x^12 + x^14.

G. C. Greubel, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Fano Plane
Index entries for linear recurrences with constant coefficients, signature (2,30,-6,-263,-250,419,666,228,-28,-17).

Cf. A111384.

R:=PowerSeriesRing(Integers(), 50); [0] cat Coefficients(R!( x*(27+784*x+1539*x^2-3286*x^3-6475*x^4-1442*x^5-3783*x^6-4444*x^7 -986*x^8)/((1-x-x^2)*(1+3*x+x^2)*(1-5*x-3*x^2+x^3)*(1+x-11*x^2 -17*x^3)) )); // G. C. Greubel, Jul 22 2023

M = {{0,1,0,0,0,1,1,1,0,0,0,0,0,0}, {1,0,1,1,0,1,1,0,1,0,0,0,0,0}, {0, 1,0,1,0,0,1,0,0,1,0,0,0,0}, {0,1,1,0,1,1,1,0,0,0,1,0,0,0}, {0,0,0,1, 0,1,1,0,0,0,0,1,0,0}, {1,1,0,1,1,0,1,0,0,0,0,0,1,0}, {1,1,1,1,1,1,0, 0,0,0,0,0,0,1}, {1,0,0,0,0,0,0,0,1,0,0,0,1,1}, {0,1,0,0,0,0,0,1,0,1, 1,0,1,1}, {0,0,1,0,0,0,0,0,1,0,1,0,0,1}, {0,0,0,1,0,0,0,0,1,1,0,1,1, 1}, {0,0,0,0,1,0,0,0,0,0,1,0,1,1}, {0,0,0,0,0,1,0,1,1,0,1,1,0,1}, {0, 0,0,0,0,0,1,1,1,1,1,1,1,0}};
v[1]= Table[Fibonacci[n], {n,0,13}]; v[n_]:= v[n]= M.v[n-1];
Table[v[n][[1]], {n,50}]
LinearRecurrence[{2,30,-6,-263,-250,419,666,228,-28,-17}, {0,27,838, 4025,29742,161630,962784,5335471,30120946,166834881}, 50] (* G. C. Greubel, Jul 22 2023 *)

def f(x): return x*(27+784*x+1539*x^2-3286*x^3-6475*x^4-1442*x^5-3783*x^6-4444*x^7 -986*x^8)/((1-x-x^2)*(1+3*x+x^2)*(1-5*x-3*x^2+x^3)*(1+x-11*x^2 -17*x^3))
def A120715_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(x) ).list()
A120715_list(50) # G. C. Greubel, Jul 22 2023

G.f.: x*(27 +784*x +1539*x^2 -3286*x^3 -6475*x^4 -1442*x^5 -3783*x^6 -4444*x^7 -986*x^8)/((1 -x -x^2)*(1 +3*x +x^2)*(1 -5*x -3*x^2 +x^3)*(1 +x -11*x^2 -17*x^3)). - Colin Barker, Nov 29 2012

Edited by N. J. A. Sloane, Jul 14 2007

A135599 Word obtained from axiom 2 using the morphism 1-> 267, 2-> 13467, 3-> 247, 4-> 23567, 5-> 467, 6-> 12457, 7-> 123456.

Original entry on oeis.org

1, 3, 4, 6, 7, 1, 2, 4, 5, 7, 1, 2, 3, 4, 5, 6, 1, 3, 4, 6, 7, 2, 3, 5, 6, 7, 1, 2, 3, 4, 5, 6, 1, 3, 4, 6, 7, 2, 4, 7, 4, 6, 7, 1, 2, 4, 5, 7, 1, 2, 3, 4, 5, 6, 2, 6, 7, 1, 3, 4, 6, 7, 2, 3, 5, 6, 7, 4, 6, 7, 1, 2, 3, 4, 5, 6, 2, 6, 7, 1, 3, 4, 6, 7, 2, 4, 7, 2, 3, 5, 6, 7, 4, 6, 7, 1, 2, 4, 5, 7, 1, 3, 4, 6, 7

Offset: 1

Roger L. Bagula, Feb 26 2008

Previous name was: Seven-tone substitution on a Fano projective plane graph as used in A120714 (for use in making church tone A,B,C,D,E,F,G music).
Idea inspired by a post in yahoo egroup fractals by "Dahlia Lahla" astro_girl_690(AT)yahoo.ca
In Mathematica you can transfer this to a 12-tone MIDI scale as: to letters
b = a /. 1 -> "a" /. 2 -> "b" /. 3 -> "c" /. 4 -> "d" /. 5 -> "e" /. 6 -> "f" /. 7 -> "g"
back to numbers on a 12-tone scale:
c = b /. "a" -> 1 /. "b" -> 3 /. "c" -> 4 /. "d" -> 6 /. "e" -> 8 /. "f" -> 9 /. "g" -> 11

Roger L. Bagula, Feb 26 2008, Table of n, a(n) for n = 1..314

Cf. A120714.

s[1] = {2, 6, 7}; s[2] = {1, 3, 4, 6, 7}; s[3] = {2, 4, 7}; s[4] = {2, 3, 5, 6, 7}; s[5] = {4, 6, 7}; s[6] = {1, 2, 4, 5, 7}; s[7] = {1, 2, 3, 4, 5, 6};
t[a_] := Flatten[s /@ a];
p[0] = s[1]; p[1] = t[p[0]]; p[n_] := t[p[n - 1]]; a = p[3]

Edited and new name from Joerg Arndt, Sep 26 2018

cp's OEIS Frontend

A120715 Sequence produced by 14 X 14 Markov chain based on 14-vertex graph formed from direct product of two copies of the graph used in A120714.

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