A247313 a(n) = 5*a(n-1) - 2^n for n>0, a(0)=1.

1, 3, 11, 47, 219, 1063, 5251, 26127, 130379, 651383, 3255891, 16277407, 81382939, 406906503, 2034516131, 10172547887, 50862673899, 254313238423, 1271565929971, 6357829125567, 31789144579259, 158945720799143, 794728599801411, 3973642990618447

Offset: 0

Author

Vincenzo Librandi, Sep 12 2014

Keywords

• nonn
• easy

References

• James Boswell Instituut, Sequences, 2006, p. 19 (recurrence 1.d).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-10).

Crossrefs

Cf. A000079, A000351, A074600, A085279.

Programs

Magma

[(2^(n+1)+5^n)/3: n in [0..30]];

Mathematica

RecurrenceTable[{a[0] == 1, a[n] == 5 a[n - 1] - 2^n}, a, {n, 0, 30}] (* or *) Table[(2^(n + 1) + 5^n)/3, {n, 0, 30}]

PARI

Vec((1-4*x)/((1-2*x)*(1-5*x)) + O(x^50)) \\ Michel Marcus, Sep 13 2014

Formula

G.f.: (1-4*x)/((1-2*x)*(1-5*x)).

a(n) = ( 2^(n+1) + 5^n )/3.

a(n) = 7*a(n-1) - 10*a(n-2) for n>1.