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A330395
Number of nontrivial equivalence classes of S_n under the {1234,3412} pattern-replacement equivalence.
1
1, 9, 26, 51, 85, 129, 184, 251, 331, 425, 534, 659, 801, 961, 1140, 1339, 1559, 1801, 2066, 2355, 2669, 3009, 3376, 3771, 4195, 4649, 5134, 5651, 6201, 6785, 7404, 8059, 8751, 9481, 10250, 11059, 11909, 12801, 13736, 14715, 15739, 16809, 17926, 19091, 20305, 21569, 22884, 24251
OFFSET
4,2
FORMULA
a(n) = (n^3 + 6*n^2 - 55*n + 54)/6 for n >= 7.
From Colin Barker, May 11 2020: (Start)
G.f.: x^4 + 9*x^5 + 26*x^6 + x^7*(51 - 119*x + 95*x^2 - 26*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>10.
(End)
MATHEMATICA
{1} ~ Join ~ LinearRecurrence[{4, -6, 4, -1}, { 9, 26, 51, 85}, 47] (* Greg Dresden, Jun 18 2020 *)
PROG
(PARI) a(n) = if(n<7, if(n<4, 0, [1, 9, 26][n-3]), (n^3 + 6*n^2 - 55*n + 54)/6) \\ Andrew Howroyd, May 10 2020
(PARI) Vec(x^4 + 9*x^5 + 26*x^6 + x^7*(51 - 119*x + 95*x^2 - 26*x^3) / (1 - x)^4 + O(x^40)) \\ Colin Barker, May 11 2020
CROSSREFS
Sequence in context: A352775 A085367 A343560 * A081267 A052153 A154560
KEYWORD
easy,nonn
AUTHOR
Quinn Perian, May 10 2020
STATUS
approved