|
| |
|
|
A200859
|
|
a(n) = 2*a(n-1)+3*a(n-2)+5^n with n>1, a(0)=-2, a(1)=1.
|
|
2
|
|
|
|
-2, 1, 21, 170, 1028, 5691, 30091, 155380, 791658, 4002581, 20145761, 101127390, 506832688, 2537750671, 12699515031, 63529860200, 317746156118, 1589021345961, 7945978425901, 39732507217810, 198670381353948, 993375442564451, 4966947820206371, 24834950923184220
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
REFERENCES
|
B. Satyanarayana and K. S. Prasad, Discrete Mathematics and Graph Theory, PHI Learning Pvt. Ltd. (Eastern Economy Edition), 2009, p. 81 (3.1;4)
|
|
|
LINKS
|
Bruno Berselli, Table of n, a(n) for n = 0..1000.
Index entries for sequences related to linear recurrences with constant coefficients, signature (7,-7,-15).
|
|
|
FORMULA
|
G.f.: -(2-15*x)/((1+x)*(1-3*x)*(1-5*x)).
a(n) = 7*a(n-1)-7*a(n-1)-15*a(n-3) for n>2, a(0)=-2, a(1)=1, a(2)=21.
a(n) = (50*5^n-81*3^n-17*(-1)^n)/24.
|
|
|
MATHEMATICA
|
LinearRecurrence[{7, -7, -15}, {-2, 1, 21}, 24]
|
|
|
PROG
|
(MAGMA) [n le 2 select 3*n-5 else 2*Self(n-1)+3*Self(n-2)+5^(n-1): n in [1..24]];
(PARI) for(n=0, 23, print1((50*5^n-81*3^n-17*(-1)^n)/24", "));
(Maxima) makelist(coeff(taylor(-(2-15*x)/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);
|
|
|
CROSSREFS
|
Cf. A016209, A200864.
Sequence in context: A051492 A164827 A213976 * A127607 A059360 A108778
Adjacent sequences: A200856 A200857 A200858 * A200860 A200861 A200862
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Bruno Berselli, Nov 23 2011
|
|
|
STATUS
|
approved
|
| |
|
|
