A171480 a(n) = 6*a(n-1) - 8*a(n-2) + 4 for n > 1; a(0) = 1, a(1) = 9.

1, 9, 50, 232, 996, 4124, 16780, 67692, 271916, 1089964, 4364460, 17467052, 69886636, 279583404, 1118407340, 4473776812, 17895402156, 71582198444, 286329973420, 1145322252972, 4581293730476, 18325184359084, 73300756310700

Offset

0,2

Comments

Inverse binomial transform of A016273.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Formula

a(n) = (25*4^n - 27*2^n + 8)/6.

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

E.g.f.: exp(x)*(8 - 27*exp(x) + 25*exp(3*x))/6. - Stefano Spezia, Sep 27 2023

Prog

(PARI) {m=23; v=concat([1, 9], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]+4); v}
(Magma) [(25*4^n-27*2^n+8)/6: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011

Crossrefs

Cf. A016273 (expansion of 1/((1-2*x)*(1-3*x)*(1-5*x))), A171472, A171473.

Sequence in context: A006974 A279979 A222993 * A369906 A257589 A341921

Adjacent sequences: A171477 A171478 A171479 * A171481 A171482 A171483

Keyword

nonn,easy

Author

Klaus Brockhaus, Dec 09 2009

Status

approved