A321002 a(0)=3; thereafter a(n) = 20*6^(n-1)-2^(n-1).

3, 19, 118, 716, 4312, 25904, 155488, 933056, 5598592, 33592064, 201553408, 1209322496, 7255939072, 43535642624, 261213872128, 1567283265536, 9403699658752, 56422198083584, 338533188763648, 2031199133106176, 12187194799685632, 73123168800210944, 438739012805459968, 2632434076841148416

Offset: 0

Author

N. J. A. Sloane, Nov 01 2018

Keywords

• nonn
• easy

Comments

Conjectured to be the sum of A175046(i) for 2^n <= i < 2^(n+1).

Conjecture is true (see comments in A175046). - Chai Wah Wu, Nov 18 2018

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-12).

Crossrefs

Essentially the first differences of A321003.

Cf. A175046.

Programs

PARI

Vec((1 - x)*(3 - 2*x) / ((1 - 2*x)*(1 - 6*x)) + O(x^25)) \\ Colin Barker, Nov 02 2018

PARI

a(n) = if (n, 20*6^(n-1)-2^(n-1), 3); \\ Michel Marcus, Nov 02 2018

Formula

From Colin Barker, Nov 02 2018: (Start)

G.f.: (1 - x)*(3 - 2*x) / ((1 - 2*x)*(1 - 6*x)).

a(n) = 8*a(n-1) - 12*a(n-2) for n>2.

(End)