A107584 a(n) = 4^n - 4*n.

1, 0, 8, 52, 240, 1004, 4072, 16356, 65504, 262108, 1048536, 4194260, 16777168, 67108812, 268435400, 1073741764, 4294967232, 17179869116, 68719476664, 274877906868, 1099511627696, 4398046511020, 17592186044328, 70368744177572, 281474976710560, 1125899906842524

Offset

0,3

Comments

Numbers a(n) = k such that number m with n 4's and k 1's has digit product = digit sum = 4^n.

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

From Harvey P. Dale, Oct 21 2011: (Start)

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) with a(0)=1, a(1)=0, and a(2)=8.

G.f.: (-17*x^2+6*x-1)/((x-1)^2*(4*x-1)). (End)

E.g.f.: exp(x)*(exp(3*x) - 4*x). - Elmo R. Oliveira, Sep 10 2024

Example

Corresponding numbers m are 1, 4, 1111111144, ...

Mathematica

Table[4^m-4*m, {m, 0, 20}]
LinearRecurrence[{6, -9, 4}, {1, 0, 8}, 30] (* Harvey P. Dale, Oct 21 2011 *)

Prog

(Magma) [(4^n - 4*n): n in [0..25]]; // Vincenzo Librandi, Dec 16 2010
(PARI) a(n)=4^n-4*n \\ Charles R Greathouse IV, Sep 08 2012
(Python)
def A107584(n): return (1<<(n<<1))-(n<<2) # Chai Wah Wu, Nov 29 2023

Crossrefs

Cf. A107583, A107585.

Sequence in context: A026973 A244718 A303509 * A323940 A027225 A073377

Adjacent sequences: A107581 A107582 A107583 * A107585 A107586 A107587

Keyword

nonn,easy

Author

Zak Seidov, May 16 2005

Extensions

More terms from Vincenzo Librandi, Dec 16 2010

Corrected by Charles R Greathouse IV, Sep 08 2012

Status

approved