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A102285 G.f. (1-x)/(7*x^2-6*x+1). 6
1, 5, 23, 103, 457, 2021, 8927, 39415, 174001, 768101, 3390599, 14966887, 66067129, 291634565, 1287337487, 5682582967, 25084135393, 110726731589, 488771441783, 2157541529575, 9523849084969, 42040303802789 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A floretion-generated sequence relating to the second binomial transform of Pell numbers A000129.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (6,-7).

FORMULA

a(n) = A086351(n+1) - 3*A086351(n) (FAMP result); Inversion gives A027649 (SuperSeeker result); Inverse binomial transform of A007070 (SuperSeeker result);

a(n)=((1+sqrt(2))(3+sqrt(2))^n+(1-sqrt(2))(3-sqrt(2))^n)/2 offset 0. a(n)=third binomial transform of 1,2,2,4,4. - Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009

a(0)=1, a(1)=5, a(n)=6*a(n-1)-7*a(n-2) for n>1. - Philippe Deléham, Sep 19 2009

PROG

Floretion Algebra Multiplication Program, FAMP Code: (a(n)) = jesforseq[ + .5'i + .5i' + 2'jj' + .5'ij' + .5'ji' ]; A000004 = vesforseq.

(MAGMA) [Floor(((1+Sqrt(2))*(3+Sqrt(2))^n+(1-Sqrt(2))*(3-Sqrt(2))^n)/2): n in [0..30]]; // Vincenzo Librandi, Oct 12 2011

CROSSREFS

Cf. A086351, A027649, A007070.

Sequence in context: A120902 A054441 A289803 * A218985 A129162 A167660

Adjacent sequences:  A102282 A102283 A102284 * A102286 A102287 A102288

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Feb 19 2005

STATUS

approved

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Last modified October 23 20:10 EDT 2017. Contains 293813 sequences.