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A318947
Column 2 of triangle A318945.
4
0, 0, 0, 0, 1, 6, 26, 97, 331, 1064, 3277, 9775, 28448, 81201, 228211, 633384, 1740037, 4740327, 12825008, 34500649, 92372683, 246352952, 654878173, 1736172895, 4592568896, 12125944161, 31967715811, 84170419272, 221388694261, 581807602839, 1527909651152, 4010192518105
OFFSET
0,6
LINKS
Czabarka, É., Flórez, R., Junes, L., & Ramírez, J. L., Enumerations of peaks and valleys on non-decreasing Dyck paths, Discrete Mathematics (2018), 341(10), 2789-2807.
FORMULA
Let alpha(n) = Sum_{k=0..n} binomial(2*n-1-k,k-1)*hypergeom([2,2,1-k], [1,1-2*k+2*n], -1)) then alpha(n) = a(n+3) for n >= 0. - Peter Luschny, Oct 28 2018
Conjectures from Colin Barker, Oct 28 2018: (Start)
G.f.: x^4*(1 - x)^3 / ((1 - 2*x)^3*(1 - 3*x + x^2)).
a(n) = 9*a(n-1) - 31*a(n-2) + 50*a(n-3) - 36*a(n-4) + 8*a(n-5) for n>7.
(End)
MAPLE
a := n -> `if`(n < 3, 0, combinat:-fibonacci(2*n) - (n^2 + 9*n + 28)*2^(n - 6)):
seq(a(n), n=0..31); # Peter Luschny, Oct 28 2018
PROG
(GAP) Concatenation([0, 0, 0], List([3..31], n->Fibonacci(2*n)-(n^2+9*n+28)*2^(n-6))); # Muniru A Asiru, Oct 28 2018
CROSSREFS
Cf. A318945.
Sequence in context: A106392 A143132 A055589 * A377679 A320816 A239179
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 18 2018
EXTENSIONS
More terms from Peter Luschny, Oct 28 2018
a(30) corrected by Muniru A Asiru, Oct 28 2018
STATUS
approved