The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A172172 Sums of NW-SE diagonals of triangle A172171. 2
 0, 1, 10, 20, 39, 68, 116, 193, 318, 520, 847, 1376, 2232, 3617, 5858, 9484, 15351, 24844, 40204, 65057, 105270, 170336, 275615, 445960, 721584, 1167553, 1889146, 3056708, 4945863, 8002580, 12948452, 20951041, 33899502, 54850552, 88750063, 143600624, 232350696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is the sequence A(0,1;1,1;9) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. - Wolfdieter Lang, Oct 18 2010 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences. Index entries for linear recurrences with constant coefficients, signature (2,0,-1). FORMULA a(n) = a(n-1) + a(n-2) + 9 with a(0)=0 and a(1)=1. From Wolfdieter Lang, Oct 18 2010: (Start) O.g.f.: x*(1+8*x)/((1-x)*(1-x-x^2)). a(n) = 2*a(n-1) - a(n-3), a(0)=0, a(1)=1, a(2)=10 (Observation by G. Detlefs). (End) a(n+1) - a(n) = A022099(n). - R. J. Mathar, Apr 22 2013 a(n) = -9 + ( (11 + 9*sqrt(5))*(1 + sqrt(5))^n - (11 - 9*sqrt(5))*(1 - sqrt(5))^n )/(2^(n+1)*sqrt(5)). - Colin Barker, Jul 13 2017 a(n) = Fibonacci(n+3) + 7*Fibonacci(n+1) - 9. - G. C. Greubel, Apr 25 2022 MATHEMATICA CoefficientList[Series[x*(1+8*x)/((1-x)*(1-x-x^2)), {x, 0, 50}], x] (* G. C. Greubel, Jul 13 2017 *) PROG (PARI) concat(0, Vec(x*(1+8*x)/((1-x)*(1-x-x^2)) + O(x^50))) \\ Colin Barker, Jul 13 2017 (Magma) [Lucas(n+2) +6*Fibonacci(n+1) -9: n in [0..50]]; // G. C. Greubel, Apr 25 2022 (SageMath) [fibonacci(n+3) +7*fibonacci(n+1) -9 for n in (0..50)] # G. C. Greubel, Apr 25 2022 CROSSREFS Cf. A000032, A000045, A172171. Sequence in context: A188334 A266087 A047881 * A275245 A020953 A033846 Adjacent sequences: A172169 A172170 A172171 * A172173 A172174 A172175 KEYWORD nonn,easy AUTHOR Mark Dols, Jan 28 2010 EXTENSIONS Wrong offset 1 changed into 0 Wolfdieter Lang, Oct 18 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 21:59 EDT 2023. Contains 365812 sequences. (Running on oeis4.)