This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A033817 Convolution of natural numbers n >= 1 with Lucas numbers L(k) for k >= -4. 1
 7, 10, 16, 21, 28, 36, 47, 62, 84, 117, 168, 248, 375, 578, 904, 1429, 2276, 3644, 5855, 9430, 15212, 24565, 39696, 64176, 103783, 167866, 271552, 439317, 710764, 1149972, 1860623, 3010478, 4870980, 7881333, 12752184, 20633384, 33385431, 54018674, 87403960, 141422485 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA a(n) = L(-1)*(F(n+1)-1) + L(-2)*F(n) - L(-3)*n, F(n): Fibonacci (A000045), L(n): Lucas (A000032) with L(-n)=(-1)^n*L(n) G.f.: x*(7-11*x)/((1-x-x^2)*(1-x)^2). a(n) = Lucas(n-1) + 4*n + 1. - G. C. Greubel, Jun 01 2019 MATHEMATICA Table[LucasL[n-1] +4*n+1, {n, 1, 40}] (* G. C. Greubel, Jun 01 2019 *) PROG (PARI) vector(40, n, fibonacci(n) + fibonacci(n-2) +4*n+1) \\ G. C. Greubel, Jun 01 2019 (MAGMA) [Lucas(n-1) + 4*n + 1 : n in [1..40]]; // G. C. Greubel, Jun 01 2019 (Sage) [lucas_number2(n-1, 1, -1) +4*n+1 for n in (1..40)] # G. C. Greubel, Jun 01 2019 (GAP) List([1..40], n-> Lucas(1, -1, n-1)[2] +4*n+1 ) # G. C. Greubel, Jun 01 2019 CROSSREFS Cf. A000032, A000045, A023548, A023537, A033814. Sequence in context: A234093 A287567 A301451 * A286873 A218128 A175666 Adjacent sequences:  A033814 A033815 A033816 * A033818 A033819 A033820 KEYWORD easy,nonn AUTHOR EXTENSIONS Terms a(31) onward added by G. C. Greubel, Jun 01 2019 STATUS approved

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

Last modified December 14 17:58 EST 2019. Contains 329979 sequences. (Running on oeis4.)