

A277369


a(0) = 5, a(1) = 8; for n>1, a(n) = 2*a(n1) + a(n2).


2



5, 8, 21, 50, 121, 292, 705, 1702, 4109, 9920, 23949, 57818, 139585, 336988, 813561, 1964110, 4741781, 11447672, 27637125, 66721922, 161080969, 388883860, 938848689, 2266581238, 5472011165, 13210603568, 31893218301, 76997040170, 185887298641, 448771637452, 1083430573545
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OFFSET

0,1


COMMENTS

After the first term, there are no primes in this sequence. In fact:
a(12*k) is divisible by 5,
a(12*k+1) is divisible by 2,
a(12*k+2) is divisible by 3,
a(12*k+3) is divisible by 2,
a(12*k+4) is divisible by 11,
a(12*k+5) is divisible by 2,
a(12*k+6) is divisible by 3,
a(12*k+7) is divisible by 2,
a(12*k+8) is divisible by 7,
a(12*k+9) is divisible by 2,
a(12*k+10) is divisible by 3,
a(12*k+11) is divisible by 2.
Therefore, every term is divisible by 2, 3, 5, 7, or 11.


LINKS

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

From Colin Barker, Oct 11 2016: (Start)
a(n) = (((1sqrt(2))^n*(3+5*sqrt(2))+(1+sqrt(2))^n*(3+5*sqrt(2))))/(2*sqrt(2)).
G.f.: (52*x) / (12*xx^2).
(End)


MATHEMATICA

LinearRecurrence[{2, 1}, {5, 8}, 40] (* Alonso del Arte, Oct 11 2016 *)


PROG

(PARI) lista(n) = n++; my(v=vector(max(2, n))); v[1]=5; v[2]=8; for(i=3, n, v[i]=2*v[i1] + v[i2]); v \\ David A. Corneth, Oct 11 2016
(PARI) Vec((52*x)/(12*xx^2) + O(x^40)) \\ Colin Barker, Oct 11 2016


CROSSREFS

Cf. A276849.
Sequence in context: A294124 A120036 A036381 * A140419 A292851 A138023
Adjacent sequences: A277366 A277367 A277368 * A277370 A277371 A277372


KEYWORD

nonn,easy


AUTHOR

Bobby Jacobs, Oct 11 2016


EXTENSIONS

More terms from David A. Corneth, Oct 11 2016


STATUS

approved



