A145302 a(n) = ((7 + sqrt(7))^n + (7 - sqrt(7))^n)/2.

1, 7, 56, 490, 4508, 42532, 406112, 3899224, 37532432, 361686640, 3487250816, 33630672544, 324364881344, 3128620091968, 30177356271104, 291080943932800, 2807684251672832, 27082179878242048, 261227779725129728, 2519737361265650176, 24304756309263653888, 234437619156533847040

Offset

0,2

Comments

Binomial transform is A152265, inverse binomial transform is A146966.

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-42).

Formula

From R. J. Mathar, Oct 10 2008: (Start)

a(n) = 14*a(n-1) - 42*a(n-2).

G.f.: (1-7x)/(1-14x+42x^2). (End)

a(n) = Sum_{k=0..n} 7^k*A098158(n,k). - Philippe Deléham, Oct 14 2008

Mathematica

LinearRecurrence[{14, -42}, {1, 7}, 25] (* Paolo Xausa, May 17 2026 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((7+r7)^n+(7-r7)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008, Jul 09 2009
(PARI) a(n)=([0, 1; -42, 14]^n*[1; 7])[1, 1] \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A098158, A152265, A146966.

Sequence in context: A264912 A323216 A024091 * A233669 A265233 A165322

Adjacent sequences: A145299 A145300 A145301 * A145303 A145304 A145305

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

Extensions

More terms from R. J. Mathar, Oct 10 2008

Edited by Klaus Brockhaus, Jul 09 2009

More terms from Paolo Xausa, May 17 2026

Status

approved