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 A023861 a(n) = 1*t(n) + 2*t(n-1) + ... + k*t(n+1-k), where k=floor((n+1)/2) and t = A000032 (Lucas numbers). 1
 1, 3, 10, 15, 37, 61, 126, 203, 384, 622, 1114, 1802, 3119, 5047, 8542, 13821, 23047, 37291, 61568, 99619, 163376, 264348, 431588, 698324, 1136685, 1839195, 2987682, 4834171, 7842313, 12689129, 20566754, 33277707, 53905168, 87220394, 141229566, 228514238, 369921435 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA Conjecture: G.f.: x*(-1-3*x^5+x^4+2*x^3-4*x^2-2*x)/((x^2+x-1)* (x^4+x^2-1)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009 MATHEMATICA Table[Sum[j*LucasL[n+1-j], {j, 1, Floor[(n+1)/2]}], {n, 1, 50}] (* G. C. Greubel, Jun 12 2019 *) PROG (PARI) lucas(n) = fibonacci(n-1)+fibonacci(n+1); a(n) = sum(j=1, floor((n+1)/2), j*lucas(n+1-j)); \\ G. C. Greubel, Jun 12 2019 (MAGMA) [(&+[j*Lucas(n+1-j): j in [1..Floor((n+1)/2)]]): n in [1..50]]; // G. C. Greubel, Jun 12 2019 (Sage) [sum(j*lucas_number2(n+1-j, 1, -1) for j in (1..floor((n+1)/2))) for n in (1..50)] # G. C. Greubel, Jun 12 2019 CROSSREFS Sequence in context: A233312 A330940 A020330 * A037345 A217278 A175336 Adjacent sequences:  A023858 A023859 A023860 * A023862 A023863 A023864 KEYWORD nonn AUTHOR EXTENSIONS Title simplified by Sean A. Irvine, Jun 12 2019 Terms a(30) onward added by G. C. Greubel, Jun 12 2019 STATUS approved

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Last modified September 16 11:30 EDT 2021. Contains 347472 sequences. (Running on oeis4.)