A016214 Expansion of g.f. 1/((1-x)*(1-3*x)(1-8*x)).

1, 12, 109, 912, 7417, 59700, 478693, 3832824, 30672433, 245408988, 1963360477, 15707149536, 125657993449, 1005266339076, 8042137887061, 64337124619848, 514697061528865, 4117576685941164, 32940614068660045, 263524914292672560, 2108199319571557081, 16865594572262986452

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (12,-35,24).

Formula

a(n) = 11*a(n-1) - 24*a(n-2) + 1 with a(0) = 1, a(1) = 12. - Vincenzo Librandi, Feb 10 2011

a(n) = (2*8^(n+2) - 7*3^(n+2) + 5)/70. - Yahia Kahloune, May 19 2013

E.g.f.: exp(x)*(5 - 63*exp(2*x) + 128*exp(7*x))/70. - Stefano Spezia, Oct 25 2023

Maple

a:=n->sum((8^(n-j+1)-3^(n-j+1))/5, j=0..n+1): seq(a(n), n=0..19); # Zerinvary Lajos, Jan 15 2007

Mathematica

CoefficientList[Series[1/((1-x)*(1-3*x)(1-8*x)), {x, 0, 21}], x] (* Stefano Spezia, Oct 25 2023 *)

Crossrefs

Cf. A000244, A001018.

Sequence in context: A016161 A081200 A351161 * A037581 A177071 A081183

Adjacent sequences: A016211 A016212 A016213 * A016215 A016216 A016217

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

a(19)-a(21) from Stefano Spezia, Oct 25 2023

Status

approved