A081687 -id:A081687 - cp's OEIS frontend

A081686 a(n) = 7^n - 6^n - 5^n - 4^n + 3*3^n.

1, 1, -1, 19, 467, 5611, 53459, 455659, 3648707, 28119691, 211372019, 1562038699, 11405181347, 82545287371, 593501306579, 4245828252139, 30255066944387, 214924122640651, 1522971386761139, 10770190567911979, 76039651374633827, 536127709619251531, 3775797660906839699, 26567026101757594219

Offset: 0

Paul Barry, Mar 30 2003

Binomial transform of A081685.

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

Cf. A081685, A081687.

G.f.: -(1326*x^4-886*x^3+219*x^2-24*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 12 2024: (Start)
E.g.f.: exp(3*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).
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)

a(22)-a(23) from Elmo R. Oliveira, Sep 12 2024

A081890 a(n) = 9^n - 8^n - 7^n - 6^n + 3*5^n.

Original entry on oeis.org

1, 3, 7, 33, 643, 11073, 151867, 1816713, 19996963, 208630833, 2099398027, 20597485593, 198424412083, 1885822419393, 17740469253787, 165580566245673, 1535948935336003, 14178113530908753, 130361707324735147, 1194785495130736953, 10921581632007328723, 99616564791408530913

Offset: 0

Paul Barry, Mar 30 2003

Binomial transform of A081687.

Index entries for linear recurrences with constant coefficients, signature (35,-485,3325,-11274,15120).

Cf. A081687, A081691.

LinearRecurrence[{35,-485,3325,-11274,15120},{1,3,7,33,643},30] (* Harvey P. Dale, Jun 26 2017 *)

G.f.: -(4182*x^4-2082*x^3+387*x^2-32*x+1)/((5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)). [Colin Barker, Aug 12 2012]
From Elmo R. Oliveira, Sep 12 2024: (Start)
E.g.f.: exp(5*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).
a(n) = 35*a(n-1) - 485*a(n-2) + 3325*a(n-3) - 11274*a(n-4) + 15120*a(n-5) for n > 4. (End)

a(19)-a(21) from Elmo R. Oliveira, Sep 12 2024

cp's OEIS Frontend

A081686 a(n) = 7^n - 6^n - 5^n - 4^n + 3*3^n.

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