OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Steven Finch, Cantor-solus and Cantor-multus distributions, arXiv:2003.09458 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (6,-15,23,-27,24,-16,9,-3,1).
FORMULA
G.f.: x^2*(4-7*x+4*x^2+3*x^3-x^4)/(1-2*x+x^2-x^3)^3.
a(n) = Sum_{k=1..n} k^2 * A097230(n,k). - Alois P. Heinz, Mar 03 2020
EXAMPLE
The only two 2-bitstrings without isolated 1's are 00 and 11. The bitsums squared of these are 0 and 4. Adding these give a(2)=4.
The only four 3-bitstrings without isolated 1's are 000, 011, 110 and 111. The bitsums squared of these are 0, 4, 4 and 9. Adding these give a(3)=17.
MATHEMATICA
LinearRecurrence[{6, -15, 23, -27, 24, -16, 9, -3, 1}, {0, 0, 4, 17, 46, 116, 288, 683, 1548}, 40] (* G. C. Greubel, Apr 13 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0, 0] cat Coefficients(R!( x^2*(4-7*x+4*x^2+3*x^3-x^4)/(1-2*x+x^2-x^3)^3 )); // G. C. Greubel, Apr 13 2022
(SageMath)
def A332863_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x^2*(4-7*x+4*x^2+3*x^3-x^4)/(1-2*x+x^2-x^3)^3 ).list()
A332863_list(40) # G. C. Greubel, Apr 13 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Steven Finch, Feb 27 2020
STATUS
approved