A370177 a(n) = floor(x*a(n-1)) for n > 0 where x = (7 + sqrt(77))/2, a(0) = 1.

1, 7, 55, 433, 3415, 26935, 212449, 1675687, 13216951, 104248465, 822257911, 6485544631, 51154617793, 403481136967, 3182450283319, 25101519942001, 197987791577239, 1561625180634679, 12317290805483425, 97152411902826727, 766287918958171063, 6044082316026984529

Offset

0,2

Comments

x = (7+sqrt(77))/2 = A092290 = 7.88748219...

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = 8*a(n-1) - 7*a(n-3) for n > 2, a(0) = 1, a(1) = 7, a(2) = 55.

G.f.: (1-x-x^2)/(1-8*x+7*x^3).

a(n) = 7*a(n-1) + 7*a(n-2) - 1.

a(n) = (12*A057090(n) + 6*A057090(n-1) + 1)/13.

a(n) = (6*(77+8*sqrt(77))*((7+sqrt(77))/2)^n + 6*(77-8*sqrt(77))*((7-sqrt(77))/2)^n + 77)/1001.

a(n) = Sum_{k = 0..n} A370174(n,k)*6^k.

Crossrefs

Cf. A057090, A092290, A370174.

Sequence in context: A172743 A015564 A070997 * A122372 A342935 A083068

Adjacent sequences: A370174 A370175 A370176 * A370178 A370183 A370184

Keyword

nonn,easy

Author

Philippe Deléham, Mar 29 2024

Status

approved