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

Offset: 0

Author

Jwalin Bhatt, Apr 01 2025

Keywords

• nonn
• easy

Links

• Wikipedia, Supergolden ratio
• Index entries for linear recurrences with constant coefficients, signature (1,0,1).

Crossrefs

Cf. A000930, A001609, A092526, A169985, A205579.

Programs

Mathematica

r = Root[x^3-x^2-1, 1]; Table[Round[r^i], {i,0,120 }]
CoefficientList[Series[(1+x^2+x^4-x^8)/(1-x-x^3), {x,0,120}], x]

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.