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 A332863 Total binary weight squared of all A005251(n) binary sequences of length n not containing any isolated 1's. 2
 0, 0, 4, 17, 46, 116, 288, 683, 1548, 3403, 7320, 15461, 32146, 65954, 133800, 268804, 535434, 1058533, 2078732, 4057858, 7878814, 15223495, 29285368, 56109673, 107108104, 203766859, 386443052, 730768044, 1378180568, 2592664120, 4866008208, 9112796113 (list; graph; refs; listen; history; text; internal format)
 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:=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. = 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 Cf. A005251, A097230, A259966. Sequence in context: A147656 A095667 A212577 * A119949 A213499 A213502 Adjacent sequences: A332860 A332861 A332862 * A332864 A332865 A332866 KEYWORD nonn,easy AUTHOR Steven Finch, Feb 27 2020 STATUS approved

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Last modified September 16 23:59 EDT 2024. Contains 375984 sequences. (Running on oeis4.)