A283716 Row n=3 of A283674.

3, 32, 746, 19748, 531698, 14349932, 387424586, 10460369588, 282429602018, 7625597747132, 205891133143226, 5559060570749828, 150094635313776338, 4052555153086085132, 109418989131780794666, 2954312706551907440468, 79766443076876804830658

Offset: 0

Author

Seiichi Manyama, Mar 15 2017

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (32,-139,108).

Crossrefs

Cf. A283674.

Programs

Mathematica

Table[1 + 4^n + 27^n, {n, 0, 20}] (* Bruno Berselli, Mar 15 2017 *)
CoefficientList[Series[(3 - 64*x + 139*x^2)/((1 - x)*(1 - 4*x)*(1 - 27*x)), {x, 0, 17}], x] (* Indranil Ghosh, Mar 15 2017 *)

PARI

Vec((3 - 64*x + 139*x^2)/((1 - x)*(1 - 4*x)*(1 - 27*x)) + O(x^17)) \\ Indranil Ghosh, Mar 15 2017

PARI

a(n) = 1 + 4^n + 27^n \\ Indranil Ghosh, Mar 15 2017

Python

def A283716(n): return 1 + 4**n + 27**n # Indranil Ghosh, Mar 15 2017

Formula

G.f.: (3 - 64*x + 139*x^2)/((1 - x)*(1 - 4*x)*(1 - 27*x)).

a(n) = 32*a(n-1) - 139*a(n-2) + 108*a(n-3) for n > 2.

a(n) = 1 + 4^n + 27^n.

Extensions

Extended by Bruno Berselli, Mar 15 2017