The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A275046 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A275046

Number of binary strings with n zeros and n ones avoiding the substrings 10101101 and 1110101.
(history; published version)

#56 by Alois P. Heinz at Fri Oct 27 21:46:23 EDT 2023

STATUS

editing

approved

#55 by Alois P. Heinz at Fri Oct 27 21:46:19 EDT 2023

LINKS

Gheorghe Coserea and Alois P. Heinz, <a href="/A275046/b275046.txt">Table of n, a(n) for n = 0..1000</a> (first 253 terms from Gheorghe Coserea)

STATUS

approved

editing

#54 by Bruno Berselli at Mon Aug 20 11:22:11 EDT 2018

STATUS

proposed

approved

#53 by Jean-François Alcover at Mon Aug 20 11:18:07 EDT 2018

STATUS

editing

proposed

#52 by Jean-François Alcover at Mon Aug 20 11:17:58 EDT 2018

MATHEMATICA

a[n_] := SeriesCoefficient[(1 + x^2 y^3 + x^2 y^4 + x^3 y^4 - x^3 y^6) / (1 - x - y + x^2 y^3 - x^3 y^3 - x^4 y^4 - x^3 y^6 + x^4 y^6), {x, 0, n}, {y, 0, n}]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Aug 20 2018 *)

STATUS

approved

editing

#51 by N. J. A. Sloane at Sat Jul 28 12:03:23 EDT 2018

STATUS

proposed

approved

#50 by Gheorghe Coserea at Wed Jul 18 13:28:46 EDT 2018

STATUS

editing

proposed

Discussion

Wed Jul 18

13:32

Gheorghe Coserea: if not ok, I will add F=... at the start of second PARI prog.

#49 by Gheorghe Coserea at Wed Jul 18 13:27:06 EDT 2018

PROG

(PARI)

(PARI) r1 = (1+x^2*y^3+x^2*y^4+x^3*y^4-x^3*y^6);

Discussion

Wed Jul 18

13:28

Gheorghe Coserea: I made F shared between test and second PARI program in order to avoid having it duplicated

#48 by Gheorghe Coserea at Wed Jul 18 13:26:46 EDT 2018

PROG

(PARI) r1 = (1+x^2*y^3+x^2*y^4+x^3*y^4-x^3*y^6);

r1 = (1+x^2*y^3+x^2*y^4+x^3*y^4-x^3*y^6);

\\ test: y = Ser(diag(r1/r2, 100)); 0 =F = (x + 1)*(4*x^20 + 8*x^19 - 23*x^18 - 63*x^17 - 62*x^16 - 26*x^15 + 43*x^14 + 11*x^13 + 182*x^12 + 56*x^11 - x^10 + 203*x^9 - 66*x^8 - 154*x^7 + 286*x^6 - 368*x^5 + 233*x^4 - 75*x^3 - 8*x^2 + 20*x - 4)*(y^4 - y^3) - (12*x^17 + 48*x^16 + 72*x^15 + 49*x^14 - 23*x^13 - 57*x^12 - 91*x^11 - 137*x^10 - 84*x^9 - 34*x^8 - 91*x^7 + 62*x^6 + 24*x^5 - 34*x^4 + 41*x^3 - 10*x^2 - 3*x - 3)*y^2 + (x^15 + 4*x^14 + 6*x^13 + 3*x^12 - 6*x^11 - 11*x^10 - 11*x^9 - 8*x^8 - 3*x^7 + 12*x^6 + 11*x^4 + 5*x^3 - 6*x^2 - 4)*y - x^4 + x + 1;

\\ test: y = Ser(diag(r1/r2, 100)); 0 == subst(F, 'y, y)

x='x; y='y; t='t;

F = (x + 1)*(4*x^20 + 8*x^19 - 23*x^18 - 63*x^17 - 62*x^16 - 26*x^15 + 43*x^14 + 11*x^13 + 182*x^12 + 56*x^11 - x^10 + 203*x^9 - 66*x^8 - 154*x^7 + 286*x^6 - 368*x^5 + 233*x^4 - 75*x^3 - 8*x^2 + 20*x - 4)*(y^4 - y^3) - (12*x^17 + 48*x^16 + 72*x^15 + 49*x^14 - 23*x^13 - 57*x^12 - 91*x^11 - 137*x^10 - 84*x^9 - 34*x^8 - 91*x^7 + 62*x^6 + 24*x^5 - 34*x^4 + 41*x^3 - 10*x^2 - 3*x - 3)*y^2 + (x^15 + 4*x^14 + 6*x^13 + 3*x^12 - 6*x^11 - 11*x^10 - 11*x^9 - 8*x^8 - 3*x^7 + 12*x^6 + 11*x^4 + 5*x^3 - 6*x^2 - 4)*y - x^4 + x + 1;

STATUS

proposed

editing

#47 by Gheorghe Coserea at Wed Jul 18 10:51:49 EDT 2018

STATUS

editing

proposed

Discussion

Wed Jul 18

11:09

Gheorghe Coserea: I guess this can be seen as a performance bug for PARI ...

11:29

Gheorghe Coserea: off topic problem: devise an algorithm that optimize a multi-substitution (i.e. substvec(expr, [x1, x2, .., xn], [v1, v2, .., vn])) ... probably it is solved in some compiler book with dynamic programming or some greedy strategy; any idea ?