OFFSET
0,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1285
Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).
FORMULA
a(n) = 1 + (45*2^(2*n+2) + 45*2^(n+2) + 40*3^(n+1) + 5*2^(n+3)*3^(n+1) + 24*5^(n+1))/120.
From Colin Barker, Mar 08 2017: (Start)
G.f.: (7 - 123*x + 822*x^2 - 2589*x^3 + 3797*x^4 - 2034*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)).
a(n) = 1 + 3*2^(n-1) + 3*2^(2*n-1) + 3^n + 5^n + 6^n.
a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6) for n>5. (End)
PROG
(Ruby)
def A283457(n)
(0..n).map{|i| 1 + (45 * 2 ** (2 * i + 2) + 45 * 2 ** (i + 2) + 40 * 3 ** (i + 1) + 5 * 2 ** (i + 3) * 3 ** (i + 1) + 24 * 5 ** (i + 1)) / 120}
end
(PARI) Vec((7 - 123*x + 822*x^2 - 2589*x^3 + 3797*x^4 - 2034*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)) + O(x^30)) \\ Colin Barker, Mar 08 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 08 2017
STATUS
approved