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A080961 Fourth binomial transform of A010686 (period 2: repeat 1,5). 4
1, 9, 57, 321, 1713, 8889, 45417, 230001, 1158753, 5820009, 29178777, 146130081, 731358993, 3658920729, 18300980937, 91524036561, 457677578433, 2288560079049, 11443316955897, 57218134461441, 286095321353073 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,-15).

FORMULA

a(n) = 5*a(n-1) + 4*3^(n-1).

a(n) = 3*5^n - 2*3^n.

G.f.: (1+x)/((1-3*x)*(1-5*x)). - Klaus Brockhaus, Nov 26 2009

From Mario C. Enriquez, Dec 08 2016: (Start)

a(n) = A005059(n+1) + A005059(n) = (5^(n+1)+5^n-3^(n+1)-3^n)/2.

a(n) = Sum_{k=0..n} A003948(n-k)*3^k = Sum_{k=0..n} (3^k * ceiling(Sum_{v=0..n-k} (5^v - 5^(v-2)))). (End)

a(n) = 8*a(n-1) - 15*a(n-2) for n > 1. - Wesley Ivan Hurt, Dec 08 2016

EXAMPLE

G.f. = 1 + 9*x + 57*x^2 + 321*x^3 + 1713*x^4 + 8889*x^5 + 45417*x^6 + 230001*x^7 + ...

MAPLE

A080961:=n->3*5^n-2*3^n: seq(A080961(n), n=0..30); # Wesley Ivan Hurt, Dec 08 2016

MATHEMATICA

CoefficientList[Series[(1 + x)/((1 - 3*x) * (1 - 5*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 07 2012 *)

PROG

(MAGMA) binomtf:=func< V | [ &+[ Binomial(i-1, k-1)*V[k]: k in [1..i] ]: i in [1..#V] ] >;

binomtf(binomtf(binomtf(binomtf(&cat[ [1, 5]: n in [1..11] ])))); // Klaus Brockhaus, Nov 26 2009

(MAGMA) [3*5^n - 2*3^n: n in [0..30]]; // Vincenzo Librandi, Dec 07 2012

CROSSREFS

Cf. A010686, A080960, A080962.

Sequence in context: A014916 A045635 A026896 * A163919 A262490 A180028

Adjacent sequences:  A080958 A080959 A080960 * A080962 A080963 A080964

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 03 2003

EXTENSIONS

Definition corrected, edited by Klaus Brockhaus, Nov 26 2009

STATUS

approved

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Last modified September 17 10:52 EDT 2019. Contains 327129 sequences. (Running on oeis4.)