A081680 a(n) = (7^n - 6^n - 5^n - 4^n + 4*3^n)/2.

1, 2, 4, 23, 274, 2927, 27094, 228923, 1827634, 14069687, 105715534, 781107923, 5702856394, 41273440847, 296753044774, 2122921300523, 15127554995554, 107462125890407, 761485887090814, 5385095865086723, 38019827430709114, 268063860039802367, 1887898846143949654, 13283513097950386523

Offset

0,2

Comments

Binomial transform of A081679.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (25,-245,1175,-2754,2520).

Formula

G.f.: -(1083*x^4-762*x^3+199*x^2-23*x+1)/((3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). [Colin Barker, Sep 07 2012]

From Elmo R. Oliveira, Sep 13 2024: (Start)

E.g.f.: exp(3*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 4)/2.

a(n) = 25*a(n-1) - 245*a(n-2) + 1175*a(n-3) - 2754*a(n-4) + 2520*a(n-5) for n > 4. (End)

Mathematica

LinearRecurrence[{25, -245, 1175, -2754, 2520}, {1, 2, 4, 23, 274}, 30] (* Harvey P. Dale, Feb 19 2018 *)

Crossrefs

Cf. A081679, A081681.

Sequence in context: A009313 A009317 A209024 * A269573 A147761 A214299

Adjacent sequences: A081677 A081678 A081679 * A081681 A081682 A081683

Keyword

easy,nonn

Author

Paul Barry, Mar 30 2003

Extensions

a(21)-a(23) from Elmo R. Oliveira, Sep 13 2024

Status

approved