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A261473
Number of binary strings of length n+6 such that the smallest number whose binary representation is not visible in the string is 8.
2
0, 2, 10, 40, 116, 296, 699, 1557, 3325, 6893, 13964, 27789, 54536, 105854, 203645, 388970, 738596, 1395718, 2626914, 4927664, 9217604, 17201570, 32036763, 59564873, 110586325, 205056292, 379823379, 702897160, 1299744979, 2401747773, 4435467036, 8187063102
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,-2,-5,-6,10,21,0,-29,-33,11,44,30,-16,-36,-17,9,16,6,-2,-3,-1).
FORMULA
G.f.: (x^16 +5*x^15 +11*x^14 +10*x^13 -9*x^12 -40*x^11 -52*x^10 -19*x^9 +36*x^8 +61*x^7 +31*x^6 -13*x^5 -26*x^4 -14*x^3 +4*x^2 +2*x+2) *x / ((x+1) *(x^2+x+1) *(x^3+x^2-1) *(x^2+x-1) *(x^3+x^2+x-1) *(x^4+x^3-1) *(x^3+x-1) *(x-1)^3).
a(n) = A261019(n+6,8).
MATHEMATICA
CoefficientList[Series[(x^16+5x^15+11x^14+10x^13-9x^12-40x^11-52x^10-19x^9+36x^8+61x^7+31x^6-13x^5-26x^4- 14x^3+ 4x^2+ 2x+2)x/((x+1)(x^2+x+1)(x^3+x^2-1)(x^2+x-1)(x^3+x^2+x-1)(x^4+x^3-1)(x^3+x-1)(x-1)^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -2, -5, -6, 10, 21, 0, -29, -33, 11, 44, 30, -16, -36, -17, 9, 16, 6, -2, -3, -1}, {0, 2, 10, 40, 116, 296, 699, 1557, 3325, 6893, 13964, 27789, 54536, 105854, 203645, 388970, 738596, 1395718, 2626914, 4927664, 9217604}, 40] (* Harvey P. Dale, Oct 30 2024 *)
CROSSREFS
Column k=8 of A261019.
Sequence in context: A339090 A244376 A009338 * A377946 A174395 A320526
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Aug 20 2015
STATUS
approved