A115164 a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 3, a(1) = 7, a(3) = 9, for n > 2.

3, 7, 9, 55, 201, 823, 3273, 13111, 52425, 209719, 838857, 3355447, 13421769, 53687095, 214748361, 858993463, 3435973833, 13743895351, 54975581385, 219902325559, 879609302217, 3518437208887, 14073748835529, 56294995342135

Offset: 0

Author

Roger L. Bagula, Mar 06 2006

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,4).

Crossrefs

Cf. A115113, A115335.

Programs

Magma

[3] cat [(4^(1+n) -19*(-1)^n)/5: n in [1..50]]; // G. C. Greubel, Nov 23 2018

Mathematica

Join[{3}, LinearRecurrence[{3, 4}, {7, 9}, 50]]

Maxima

(a[0] : 3, a[1] : 7, a[2] : 9, a[n] := 3*a[n-1] + 4*a[n-2], makelist(a[n], n, 0, 50)); /* Franck Maminirina Ramaharo, Nov 23 2018 */

PARI

vector(50, n, n--; if(n==0, 3, (4^(1+n) -19*(-1)^n)/5)) \\ G. C. Greubel, Nov 23 2018

Sage

[3] + [(4^(1+n) -19*(-1)^n)/5 for n in (1..50)] # G. C. Greubel, Nov 23 2018

Formula

From Colin Barker, Oct 31 2012: (Start)

a(n) = (4^(1 + n) - 19*(-1)^n)/5 for n > 0.

a(n) = 3*a(n-1) + 4*a(n-2) for n > 2.

G.f.: (24*x^2 + 2*x - 3)/((x + 1)*(4*x - 1)). (End)

From Franck Maminirina Ramaharo, Nov 23 2018: (Start)

a(n) = A115113(n) + A165326(n).

E.g.f.: (30 - 19*exp(-x) + 4*exp(4*x))/5. (End)

Extensions

Edited, and new name from Franck Maminirina Ramaharo, Nov 23 2018, after Colin Barker