A288689 Number of n-digit biquanimous strings using digits {0,1,...,5}.
1, 1, 6, 46, 376, 2841, 19718, 128535, 805848, 4942711, 29970542, 180700389, 1086570460, 6525662885, 39170135870, 235062159691, 1410477973872, 8463133736523, 50779476069198, 304678570340665, 1828075815690100, 10968466276145161, 65810827526263678
Offset: 0
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (23, -231, 1351, -5153, 13557, -25301, 33829, -32226, 21368, -9376, 2448, -288).
Crossrefs
Column k=5 of A288638.
Programs
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Mathematica
CoefficientList[Series[(144x^14-1224x^13+4976x^12-11002x^11+18115x^10-25255x^9+30319x^8-29516x^7+21747x^6-11691x^5+4506x^4-1212x^3+214x^2-22x+1)/((6x-1)(3x-1)(2x-1)^4(x-1)^6),{x,0,40}],x] (* or *) LinearRecurrence[{23,-231,1351,-5153,13557,-25301,33829,-32226,21368,-9376,2448,-288},{1,1,6,46,376,2841,19718,128535,805848,4942711,29970542,180700389,1086570460,6525662885,39170135870},40] (* Harvey P. Dale, Aug 18 2025 *)
Formula
G.f.: (144*x^14 -1224*x^13 +4976*x^12 -11002*x^11 +18115*x^10 -25255*x^9 +30319*x^8 -29516*x^7 +21747*x^6 -11691*x^5 +4506*x^4 -1212*x^3 +214*x^2 -22*x +1) / ((6*x-1) *(3*x-1) *(2*x-1)^4 *(x-1)^6).
Comments