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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A192968 Coefficient of x in the reduction by x^2 -> x+1 of the polynomial p(n,x) defined at Comments. 3
 0, 1, 1, 3, 7, 16, 33, 64, 118, 210, 364, 619, 1038, 1723, 2839, 4653, 7597, 12370, 20103, 32626, 52900, 85716, 138826, 224773, 363852, 588901, 953053, 1542279, 2495683, 4038340, 6534429, 10573204, 17108098, 27681798, 44790424, 72472783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The titular polynomials are defined recursively: p(n,x) = x*p(n-1,x) + n(n-1)/2, with p(0,x)=1. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232 and A192744. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-5,1,2,-1). FORMULA a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5). G.f.: x*(1 -3*x +4*x^2 -x^3)/((1-x-x^2)*(1-x)^3). - R. J. Mathar, May 11 2014 a(n) = 3*Fibonacci(n+2) -(n^2+3*n+6)/2. - G. C. Greubel, Jul 11 2019 MATHEMATICA Table[3*Fibonacci[n+2] -(n^2+3*n+6)/2, {n, 0, 40}] (* G. C. Greubel, Jul 11 2019 *) PROG (PARI) vector(40, n, n--; 3*fibonacci(n+2) -(n^2+3*n+6)/2) \\ G. C. Greubel, Jul 11 2019 (Magma) [3*Fibonacci(n+2) -(n^2+3*n+6)/2: n in [0..40]]; // G. C. Greubel, Jul 11 2019 (Sage) [3*fibonacci(n+2) -(n^2+3*n+6)/2 for n in (0..40)] # G. C. Greubel, Jul 11 2019 (GAP) List([0..40], n-> 3*Fibonacci(n+2) -(n^2+3*n+6)/2); # G. C. Greubel, Jul 11 2019 CROSSREFS Cf. A000045, A192232, A192744, A192951, A192967. Sequence in context: A084631 A219846 A229914 * A277968 A217942 A002936 Adjacent sequences: A192965 A192966 A192967 * A192969 A192970 A192971 KEYWORD nonn AUTHOR Clark Kimberling, Jul 13 2011 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 19:35 EDT 2023. Contains 365793 sequences. (Running on oeis4.)