A245807 a(n) = 7^n + 10^n.

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (17,-70).

Formula

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).

E.g.f.: e^(7*x) + e^(10*x).

a(n) = 17*a(n-1)-70*a(n-2).

a(n) = A000420(n) + A011557(n).

Mathematica

Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

Prog

(Magma) [7^n+10^n: n in [0..25]]; /* or */ I:=[2, 17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];

Crossrefs

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

Sequence in context: A110815 A273340 A074624 * A295946 A176934 A126037

Adjacent sequences: A245804 A245805 A245806 * A245808 A245809 A245810

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 04 2014

Status

approved