A283457 Row n=5 of A144048.

7, 24, 101, 477, 2411, 12729, 69251, 385017, 2175491, 12444489, 71865251, 418096857, 2446626371, 14383667049, 84875140451, 502327573497, 2980183394051, 17715498038409, 105478120962851, 628846706246937, 3753178627502531, 22420395331846569

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

Sequence in context: A196352 A050191 A321390 * A129797 A188120 A007750

Adjacent sequences: A283454 A283455 A283456 * A283458 A283459 A283460

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 08 2017

Status

approved