

A107584


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


8



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
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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

a(0)=1, a(1)=0, a(2)=8, a(n) = 6*a(n1)  9*a(n2) + 4*a(n3).  Harvey P. Dale, Oct 21 2011
G.f.: (17*x^2+6*x1)/((x1)^2*(4 x1)).  Harvey P. Dale, Oct 21 2011


EXAMPLE

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


MATHEMATICA

Table[4^m4*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^n4*n \\ Charles R Greathouse IV, Sep 08 2012


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



