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A200859 a(n) = 2*a(n-1)+3*a(n-2)+5^n for 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 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.

MAPLE

A200859:=n->(50*5^n-81*3^n-17*(-1)^n)/24; seq(A200859(n), n=0..30); # Wesley Ivan Hurt, Dec 26 2013

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);

(Sage)

def lr(a0, a1, a2, a3, a4, a5):

    x, y, z = a0, a1, a2

    while true:

       yield x

       x, y, z = y, z, a5*x+a4*y+a3*z

A200859 = lr(-2, 1, 21, 7, -7, -15)

print [A200859.next() for n in range(24)] # Bruno Berselli, May 09 2014

CROSSREFS

Cf. A016209, A200864.

Sequence in context: A051492 A164827 A213976 * A127607 A255861 A059360

Adjacent sequences:  A200856 A200857 A200858 * A200860 A200861 A200862

KEYWORD

sign,easy

AUTHOR

Bruno Berselli, Nov 23 2011

STATUS

approved

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Last modified October 22 18:55 EDT 2018. Contains 316500 sequences. (Running on oeis4.)