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 A180666 Golden Triangle sums: a(n)=a(n-4)+A001654(n) with a(0)=0, a(1)=1, a(2)=2 and a(3)=6. 6
 0, 1, 2, 6, 15, 41, 106, 279, 729, 1911, 5001, 13095, 34281, 89752, 234971, 615165, 1610520, 4216400, 11038675, 28899630, 75660210, 198081006, 518582802, 1357667406, 3554419410, 9305590831, 24362353076, 63781468404 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The a(n) are the Gi2 sums of the Golden Triangle A180662. See A180662 for information about these giraffe and other chess sums. LINKS Index entries for linear recurrences with constant coefficients, signature (2,2,-1,1,-2,-2,1). FORMULA a(n) = a(n-4)+A001654(n) with a(0)=0, a(1)=1, a(2)=2 and a(3)=6. G.f.: (-x)/((x^2-3*x+1)*(x-1)*(x+1)^2*(x^2+1)). a(n) = add(A180662(n-3*k,n-4*k),k=0..floor(n/4)),n=0..nmax). 120*a(n) = 8*A001519(n) -10*A087960(n) -9*(-1)^n -15 -6*(n+1)*(-1)^n. - R. J. Mathar, Aug 18 2016 MAPLE nmax:=27: with(combinat): for n from 0 to nmax do A001654(n):=fibonacci(n)*fibonacci(n+1) od: a(0):=0: a(1):=1: a(2):=2: a(3):=6: for n from 4 to nmax do a(n):=a(n-4)+A001654(n) od: seq(a(n), n=0..nmax); A180666 := proc(n)     option remember;     if n <=3 then         op(n+1, [0, 1, 2, 6]) ;     else         procname(n-4)+A001654(n) ;     end if; end proc: seq(A180666(n), n=0..100 ) ; # R. J. Mathar, Aug 18 2016 MATHEMATICA Take[Total@{#, PadLeft[Drop[#, -4], Length@ #]}, Length@ # - 4] &@ Table[Times @@ Fibonacci@ {n, n + 1}, {n, 0, 31}] (* or *) CoefficientList[Series[(-x)/((x^2 - 3 x + 1) (x - 1) (x + 1)^2 (x^2 + 1)), {x, 0, 27}], x] (* Michael De Vlieger, Aug 18 2016 *) CROSSREFS Cf. A064831, A180664, A180665, A115730, A180666. Sequence in context: A004664 A074446 A303551 * A280788 A121328 A139379 Adjacent sequences:  A180663 A180664 A180665 * A180667 A180668 A180669 KEYWORD easy,nonn AUTHOR Johannes W. Meijer, Sep 21 2010 STATUS approved

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Last modified January 29 07:03 EST 2020. Contains 331337 sequences. (Running on oeis4.)