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 A338200 The number of similarity classes of pointed reflection spaces of residue two in an n-dimensional vector space over GF(2). 0
 0, 0, 1, 2, 4, 6, 9, 12, 17, 21, 27, 33, 41, 48, 58, 67, 79, 90, 104, 117, 134, 149, 168, 186, 208, 228, 253, 276, 304, 330, 361, 390, 425, 457, 495, 531, 573, 612, 658, 701, 751, 798, 852, 903, 962, 1017, 1080, 1140, 1208, 1272, 1345, 1414, 1492, 1566, 1649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS S. Azam, M. Tomie, and Y. Yoshii, Classification of pointed reflection spaces, Osaka Journal of Mathematics. Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1). FORMULA a(n) = (1/8)*n*(n-2) + 2*(Sum_{k=3..n/2} p(k,3)) + p((n+2)/2,3) if n is even; a(n) = 2*floor((n-1)/4)*floor((n+1)/4) + 2*(Sum_{k=3..(n-1)/2} p(k,3)) + p((n+1)/2,3) + p((n+3)/2,3) if n is odd, where p(k,3) = A069905(k) is the number of partitions of k into three parts. From Andrew Howroyd, Oct 29 2020: (Start) a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10) for n > 10. G.f.: x^3*(1 + x + x^2 - x^4 - x^5)/((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). (End) MATHEMATICA F[n_] := If[EvenQ[n],   n (n - 2)/8 +    2*Sum[Length[IntegerPartitions[k, {3}]], {k, 3, n/2}] +    Length[IntegerPartitions[(n + 2)/2, {3}]],   2*Floor[(n - 1)/4]*Floor[(n + 1)/4] +    2*Sum[Length[IntegerPartitions[k, {3}]], {k, 3, (n - 1)/2}] +    Length[IntegerPartitions[(n + 1)/2, {3}]] +    Length[IntegerPartitions[(n + 3)/2, {3}]]] (* Second program: *) LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 1, 2, 4, 6, 9, 12, 17, 21}, 55] (* Jean-François Alcover, Nov 13 2020 *) PROG (PARI) concat([0, 0], Vec((1 + x + x^2 - x^4 - x^5)/((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^50))) \\ Andrew Howroyd, Oct 29 2020 CROSSREFS Cf. A069905. Sequence in context: A048171 A090178 A080548 * A194450 A080556 A229093 Adjacent sequences:  A338197 A338198 A338199 * A338201 A338202 A338203 KEYWORD nonn,easy AUTHOR Masaya Tomie, Oct 16 2020 STATUS approved

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Last modified July 28 23:26 EDT 2021. Contains 346340 sequences. (Running on oeis4.)