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A295717 a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 5, a(3) = 7. 1
1, 3, 5, 7, 14, 19, 37, 52, 97, 141, 254, 379, 665, 1012, 1741, 2689, 4558, 7119, 11933, 18796, 31241, 49525, 81790, 130291, 214129, 342372, 560597, 898873, 1467662, 2358343, 3842389, 6184348, 10059505, 16211085, 26336126, 42481675, 68948873, 111299476 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n)/a(n-1) -> (1 + sqrt(5))/2 = golden ratio (A001622), so that a( ) has the growth rate of the Fibonacci numbers (A000045).

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1, 3, -2, -2)

FORMULA

a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 3, a(2) = 5, a(3) = 7.

G.f.: (1 + 2 x - x^2 - 5 x^3)/(1 - x - 3 x^2 + 2 x^3 + 2 x^4).

MATHEMATICA

LinearRecurrence[{1, 3, -2, -2}, {1, 3, 5, 7}, 100]

CROSSREFS

Cf. A001622, A000045, A005672.

Sequence in context: A333630 A114980 A024372 * A308591 A309832 A319784

Adjacent sequences:  A295714 A295715 A295716 * A295718 A295719 A295720

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 29 2017

STATUS

approved

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Last modified August 8 12:08 EDT 2022. Contains 356009 sequences. (Running on oeis4.)