OFFSET
4,2
LINKS
Colin Barker, Table of n, a(n) for n = 4..1000
Michael Ma, New Results on Pattern-Replacement Equivalences: Generalizing a Classical Theorem and Revising a Recent Conjecture, 2017.
Quinn Perian, Bella Xu, Alexander Lu Zhang, Counting the Nontrivial Equivalence Classes of S_n under {1234,3412}-Pattern-Replacement, arXiv:2008.02380 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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
KEYWORD
easy,nonn
AUTHOR
Quinn Perian, May 10 2020
STATUS
approved