A283456 Row n=4 of A144048.

5, 13, 40, 136, 490, 1828, 6970, 26956, 105250, 413668, 1633450, 6471676, 25703410, 102269908, 407460730, 1625010796, 6485595970, 25899140548, 103467028810, 413479908316, 1652755798930, 6607533265588, 26419666417690, 105647272028236, 422494919768290

Offset

0,1

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1660

Index entries for linear recurrences with constant coefficients, signature (10,-35,50,-24).

Formula

a(n) = 1 + (9*2^(2*n+2) + 9*2^(n+2) + 8*3^(n+1))/24.

From Colin Barker, Mar 08 2017: (Start)

G.f.: (5 - 37*x + 85*x^2 - 59*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)).

a(n) = (2 + 3*2^n + 2*3^n + 3*4^n)/2.

a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4) for n>3. (End)

Mathematica

LinearRecurrence[{10, -35, 50, -24}, {5, 13, 40, 136}, 30] (* Harvey P. Dale, Aug 09 2023 *)

Prog

(Ruby)
def A283456(n)
  (0..n).map{|i| 1 + (9 * 2 ** (2 * i + 2) + 9 * 2 ** (i + 2) + 8 * 3 ** (i + 1)) / 24}
end
(PARI) Vec((5 - 37*x + 85*x^2 - 59*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Mar 08 2017

Crossrefs

Sequence in context: A026069 A054856 A261057 * A370095 A337339 A337336

Adjacent sequences: A283453 A283454 A283455 * A283457 A283458 A283459

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 08 2017

Status

approved