A382641 - OEIS

A382641

a(n) = round(c^n), where c is the supergolden ratio A092526.

1, 1, 2, 3, 5, 7, 10, 15, 21, 31, 46, 67, 98, 144, 211, 309, 453, 664, 973, 1426, 2090, 3063, 4489, 6579, 9642, 14131, 20710, 30352, 44483, 65193, 95545, 140028, 205221, 300766, 440794, 646015, 946781, 1387575, 2033590, 2980371, 4367946, 6401536, 9381907, 13749853

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..43.

Wikipedia, Supergolden ratio

Index entries for linear recurrences with constant coefficients, signature (1,0,1).

FORMULA

G.f.: (1 + x^2 + x^4 - x^8)/(1 - x - x^3).

a(n) = a(n-1) + a(n-3) for n>=9.

a(n) = round(((2/3)*cos((1/3)*arccos(29/2))+1/3)^n) = round(A092526^n).

a(n) = A001609(n) for n>=6.