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A180664 Golden Triangle sums: a(n)=a(n-1)+A001654(n+1) with a(0)=0. 8
0, 2, 8, 23, 63, 167, 440, 1154, 3024, 7919, 20735, 54287, 142128, 372098, 974168, 2550407, 6677055, 17480759, 45765224, 119814914, 313679520, 821223647, 2149991423, 5628750623, 14736260448, 38580030722, 101003831720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The a(n+1) (terms doubled) are the Kn13 sums of the Golden Triangle A180662. See A180662 for information about these knight and other chess sums.

LINKS

Table of n, a(n) for n=0..26.

Index entries for linear recurrences with constant coefficients, signature (3, 0, -3, 1).

FORMULA

a(n) = a(n-1)+A001654(n+1) with a(0)=0.

a(n+1) = add(A180662(2*n-k+2,k+2),k=0..floor(n)).

a(n) = (-15+(-1)^(-n)+(6-2*A)*A^(-n-1)+(6-2*B)*B^(-n-1))/10 with A=(3+sqrt(9-4))/2 and B=(3-sqrt(9-4))/2.

GF(x) = (2*x+2*x^2-x^3)/(1-3*x-x^4+3*x^3).

MAPLE

nmax:=26: with(combinat): for n from 0 to nmax+1 do A001654(n):=fibonacci(n) * fibonacci(n+1) od: a(0):=0: for n from 1 to nmax do a(n) := a(n-1)+A001654(n+1) od: seq(a(n), n=0..nmax);

CROSSREFS

Cf. A064831, A180664, A180665, A115730, A180666.

Sequence in context: A079460 A154144 A255942 * A294959 A290926 A018042

Adjacent sequences:  A180661 A180662 A180663 * A180665 A180666 A180667

KEYWORD

easy,nonn

AUTHOR

Johannes W. Meijer, Sep 21 2010

STATUS

approved

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Last modified January 23 19:34 EST 2020. Contains 331175 sequences. (Running on oeis4.)