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A098183
a(n) = 3*a(n-1) + a(n-3), a(0) = 1, a(1) = 1, a(2) = 4.
3
1, 1, 4, 13, 40, 124, 385, 1195, 3709, 11512, 35731, 110902, 344218, 1068385, 3316057, 10292389, 31945552, 99152713, 307750528, 955197136, 2964744121, 9201982891, 28561145809, 88648181548, 275146527535, 854000728414, 2650650366790, 8227097627905, 25535293612129
OFFSET
0,3
FORMULA
G.f.: (1-x)^2/(1-3*x-x^3).
a(n) = Sum_{k=0..floor(n/2)} binomial(n+k,3*k) * 3^k.
MAPLE
a:= proc(n) option remember;
`if`(n<2, 1, 3*a(n-1)+a(n-3))
end:
seq(a(n), n=0..30); # Alois P. Heinz, May 25 2022
CROSSREFS
Sequence in context: A076040 A261547 A091141 * A171556 A227747 A094628
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Aug 30 2004
STATUS
approved